mirror of
https://github.com/andatoshiki/toshiki-notebook.git
synced 2026-06-06 04:04:17 +00:00
43 lines
72 KiB
HTML
43 lines
72 KiB
HTML
<!DOCTYPE html>
|
||
<html lang="en-US" dir="ltr">
|
||
<head>
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width,initial-scale=1">
|
||
<title>Formulas for IPhO 日本語版: Section 12 | Toshiki's Note</title>
|
||
<meta name="description" content="Toshiki's web notebook served via Vitepress!">
|
||
<link rel="preload stylesheet" href="/assets/style.d3f1db94.css" as="style">
|
||
|
||
<script type="module" src="/assets/app.11c168a7.js"></script>
|
||
<link rel="preload" href="/assets/inter-roman-latin.2ed14f66.woff2" as="font" type="font/woff2" crossorigin="">
|
||
<link rel="modulepreload" href="/assets/chunks/framework.b7580407.js">
|
||
<link rel="modulepreload" href="/assets/chunks/theme.c3ca1c74.js">
|
||
<link rel="modulepreload" href="/assets/chunks/commonjsHelpers.725317a4.js">
|
||
<link rel="modulepreload" href="/assets/chunks/PageInfo.vue_vue_type_script_setup_true_lang.250b3e56.js">
|
||
<link rel="modulepreload" href="/assets/academic_physics_ipho-formulas-jpn_12.md.97cf4aa6.lean.js">
|
||
<link rel="stylesheet" href="https://cdnjs.toshiki.dev/ajax/libs/KaTeX/0.16.0/katex.min.css">
|
||
<link rel="stylesheet" href="https://cdnjs.toshiki.dev/ajax/libs/font-awesome/6.3.0/css/all.min.css">
|
||
<link rel="icon" href="https://r2.toshiki.dev/cdn/toshiki-notebook-favicon/favicon.ico">
|
||
<meta name="author" content="Anda Toshiki">
|
||
<meta name="keywords" content="Toshiki, Anda Toshiki, andatoshiki, GitHub, GitHub action, Vitepress, Vite, Notebook, Knowledge base, Programming, Programming Notes, Academic, Personal, Notebook, Productivity, Journal, Note-taking, Markdown, Notepad, Organization, Tutorial">
|
||
<meta name="google-site-verification" content="lm7PNJiYSPEx1dMast1Xptc0Vk0cU06o-daZSsIgr2I">
|
||
<meta name="HandheldFriendly" content="True">
|
||
<meta name="MobileOptimized" content="320">
|
||
<meta name="theme-color" content="#3c8772">
|
||
<meta property="og:type" content="website">
|
||
<meta property="og:locale" content="en-US">
|
||
<meta property="og:title" content="Toshiki's Note">
|
||
<meta property="og:description" content="Toshiki's web notebook served via Vitepress!">
|
||
<meta property="og:site" content="https://note.toshiki.dev">
|
||
<meta property="og:site_name" content="Toshiki's Note">
|
||
<meta property="og:image" content="https://note.toshiki.dev/og-cover.png">
|
||
<script>function siteruntime(){window.setTimeout("siteruntime()",1e3),X=new Date("8/24/2021 10:28:00"),Y=new Date,T=Y.getTime()-X.getTime(),M=24*60*60*1e3,a=T/M,A=Math.floor(a),b=(a-A)*24,B=Math.floor(b),c=(b-B)*60,C=Math.floor((b-B)*60),D=Math.floor((c-C)*60),siteruntime_span.innerHTML="This site has been running for: "+A+" day(s) "+B+" hour(s) "+C+" minute(s) "+D+" second(s)"}siteruntime();</script>
|
||
<script async defer data-website-id="" src=""></script>
|
||
<script id="check-dark-mode">(()=>{const e=localStorage.getItem("vitepress-theme-appearance")||"auto",a=window.matchMedia("(prefers-color-scheme: dark)").matches;(!e||e==="auto"?a:e==="dark")&&document.documentElement.classList.add("dark")})();</script>
|
||
<script id="check-mac-os">document.documentElement.classList.toggle("mac",/Mac|iPhone|iPod|iPad/i.test(navigator.platform));</script>
|
||
</head>
|
||
<body>
|
||
<div id="app"><div class="Layout" data-v-f6284a77><!--[--><!--]--><!--[--><span tabindex="-1" data-v-315fcc9b></span><a href="#VPContent" class="VPSkipLink visually-hidden" data-v-315fcc9b> Skip to content </a><!--]--><!----><header class="VPNav" data-v-f6284a77 data-v-ff202323><div class="VPNavBar has-sidebar" data-v-ff202323 data-v-57f83237><div class="container" data-v-57f83237><div class="title" data-v-57f83237><div class="VPNavBarTitle has-sidebar" data-v-57f83237 data-v-87c32abd><a class="title" href="/" data-v-87c32abd><!--[--><!--]--><!--[--><img class="VPImage logo" src="/logos/logo.png" alt data-v-6ebf9bdf><!--]--><!--[-->Toshiki's Note<!--]--><!--[--><!--]--></a></div></div><div class="content" data-v-57f83237><div class="curtain" data-v-57f83237></div><div class="content-body" data-v-57f83237><!--[--><!--]--><div class="VPNavBarSearch search" data-v-57f83237><!--[--><!----><div id="docsearch"><button type="button" class="DocSearch DocSearch-Button" aria-label="Search"><span class="DocSearch-Button-Container"><svg class="DocSearch-Search-Icon" width="20" height="20" viewBox="0 0 20 20" aria-label="search icon"><path d="M14.386 14.386l4.0877 4.0877-4.0877-4.0877c-2.9418 2.9419-7.7115 2.9419-10.6533 0-2.9419-2.9418-2.9419-7.7115 0-10.6533 2.9418-2.9419 7.7115-2.9419 10.6533 0 2.9419 2.9418 2.9419 7.7115 0 10.6533z" stroke="currentColor" fill="none" fill-rule="evenodd" stroke-linecap="round" stroke-linejoin="round"></path></svg><span class="DocSearch-Button-Placeholder">Search</span></span><span class="DocSearch-Button-Keys"><kbd class="DocSearch-Button-Key"></kbd><kbd class="DocSearch-Button-Key">K</kbd></span></button></div><!--]--></div><nav aria-labelledby="main-nav-aria-label" class="VPNavBarMenu menu" data-v-57f83237 data-v-183ec936><span id="main-nav-aria-label" class="visually-hidden" data-v-183ec936>Main Navigation</span><!--[--><!--[--><a class="VPLink link VPNavBarMenuLink" href="/development/" tabindex="0" data-v-183ec936 data-v-416f44b0><!--[--><span data-v-416f44b0>Development</span><!--]--></a><!--]--><!--[--><div class="VPFlyout VPNavBarMenuGroup active" data-v-183ec936 data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" data-v-62bba1f9><span class="text" data-v-62bba1f9><!----><span data-v-62bba1f9>Academic</span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="text-icon" data-v-62bba1f9><path d="M12,16c-0.3,0-0.5-0.1-0.7-0.3l-6-6c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l5.3,5.3l5.3-5.3c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-6,6C12.5,15.9,12.3,16,12,16z"></path></svg></span></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><div class="items" data-v-17c3596a><!--[--><!--[--><div class="VPMenuGroup" data-v-17c3596a data-v-b9d0e57b><p class="title" data-v-b9d0e57b>K-12</p><!--[--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/academic/chemistry/index" data-v-ec5470f2><!--[-->Chemistry<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/discrete-math/index" data-v-ec5470f2><!--[-->Discrete Math.<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/academic/literature/index" data-v-ec5470f2><!--[-->Literature<!--]--></a></div><!--]--><!--]--></div><!--]--><!--[--><div class="VPMenuGroup" data-v-17c3596a data-v-b9d0e57b><p class="title" data-v-b9d0e57b>Tools</p><!--[--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link active" href="/academic/physics/ipho-formulas-jpn/1" data-v-ec5470f2><!--[-->Formulas for IPhO JPN.<!--]--></a></div><!--]--><!--]--></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--]--></div><!--[--><!--]--></div></div></div><!--]--><!--[--><div class="VPFlyout VPNavBarMenuGroup" data-v-183ec936 data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" data-v-62bba1f9><span class="text" data-v-62bba1f9><!----><span data-v-62bba1f9>Application</span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="text-icon" data-v-62bba1f9><path d="M12,16c-0.3,0-0.5-0.1-0.7-0.3l-6-6c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l5.3,5.3l5.3-5.3c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-6,6C12.5,15.9,12.3,16,12,16z"></path></svg></span></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><div class="items" data-v-17c3596a><!--[--><!--[--><div class="VPMenuGroup" data-v-17c3596a data-v-b9d0e57b><p class="title" data-v-b9d0e57b>Personal projects</p><!--[--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/application/markdown-it-katex/how-to-use" data-v-ec5470f2><!--[-->markdown-it-katex<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/application/vitepress-plugin-shiki-twoslash/index" data-v-ec5470f2><!--[-->vitepress-plugin-shiki-twoslash<!--]--></a></div><!--]--><!--]--></div><!--]--><!--]--></div><!--[--><!--]--></div></div></div><!--]--><!--[--><div class="VPFlyout VPNavBarMenuGroup" data-v-183ec936 data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" data-v-62bba1f9><span class="text" data-v-62bba1f9><!----><span data-v-62bba1f9>Save</span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="text-icon" data-v-62bba1f9><path d="M12,16c-0.3,0-0.5-0.1-0.7-0.3l-6-6c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l5.3,5.3l5.3-5.3c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-6,6C12.5,15.9,12.3,16,12,16z"></path></svg></span></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><div class="items" data-v-17c3596a><!--[--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><a class="VPLink link" href="/save/reading/index" data-v-ec5470f2><!--[-->Reading<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><a class="VPLink link" href="/academic/vocabulary/index" data-v-ec5470f2><!--[-->Vocabulary<!--]--></a></div><!--]--><!--]--></div><!--[--><!--]--></div></div></div><!--]--><!--]--></nav><!----><div class="VPNavBarAppearance appearance" data-v-57f83237 data-v-dc7cad42><button class="VPSwitch VPSwitchAppearance" type="button" role="switch" title="toggle dark mode" aria-checked="false" data-v-dc7cad42 data-v-65b67168 data-v-56eb52d1><span class="check" data-v-56eb52d1><span class="icon" data-v-56eb52d1><!--[--><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="sun" data-v-65b67168><path d="M12,18c-3.3,0-6-2.7-6-6s2.7-6,6-6s6,2.7,6,6S15.3,18,12,18zM12,8c-2.2,0-4,1.8-4,4c0,2.2,1.8,4,4,4c2.2,0,4-1.8,4-4C16,9.8,14.2,8,12,8z"></path><path d="M12,4c-0.6,0-1-0.4-1-1V1c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,3.6,12.6,4,12,4z"></path><path d="M12,24c-0.6,0-1-0.4-1-1v-2c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,23.6,12.6,24,12,24z"></path><path d="M5.6,6.6c-0.3,0-0.5-0.1-0.7-0.3L3.5,4.9c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C6.2,6.5,5.9,6.6,5.6,6.6z"></path><path d="M19.8,20.8c-0.3,0-0.5-0.1-0.7-0.3l-1.4-1.4c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C20.3,20.7,20,20.8,19.8,20.8z"></path><path d="M3,13H1c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S3.6,13,3,13z"></path><path d="M23,13h-2c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S23.6,13,23,13z"></path><path d="M4.2,20.8c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C4.7,20.7,4.5,20.8,4.2,20.8z"></path><path d="M18.4,6.6c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C18.9,6.5,18.6,6.6,18.4,6.6z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="moon" data-v-65b67168><path d="M12.1,22c-0.3,0-0.6,0-0.9,0c-5.5-0.5-9.5-5.4-9-10.9c0.4-4.8,4.2-8.6,9-9c0.4,0,0.8,0.2,1,0.5c0.2,0.3,0.2,0.8-0.1,1.1c-2,2.7-1.4,6.4,1.3,8.4c2.1,1.6,5,1.6,7.1,0c0.3-0.2,0.7-0.3,1.1-0.1c0.3,0.2,0.5,0.6,0.5,1c-0.2,2.7-1.5,5.1-3.6,6.8C16.6,21.2,14.4,22,12.1,22zM9.3,4.4c-2.9,1-5,3.6-5.2,6.8c-0.4,4.4,2.8,8.3,7.2,8.7c2.1,0.2,4.2-0.4,5.8-1.8c1.1-0.9,1.9-2.1,2.4-3.4c-2.5,0.9-5.3,0.5-7.5-1.1C9.2,11.4,8.1,7.7,9.3,4.4z"></path></svg><!--]--></span></span></button></div><div class="VPSocialLinks VPNavBarSocialLinks social-links" data-v-57f83237 data-v-aaebde08 data-v-8a65be56><!--[--><a class="VPSocialLink no-icon" href="https://github.com/andatoshiki" aria-label="github" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>GitHub</title><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"/></svg></a><a class="VPSocialLink no-icon" href="https://twitter.com/andatoshiki" aria-label="twitter" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>Twitter</title><path d="M21.543 7.104c.015.211.015.423.015.636 0 6.507-4.954 14.01-14.01 14.01v-.003A13.94 13.94 0 0 1 0 19.539a9.88 9.88 0 0 0 7.287-2.041 4.93 4.93 0 0 1-4.6-3.42 4.916 4.916 0 0 0 2.223-.084A4.926 4.926 0 0 1 .96 9.167v-.062a4.887 4.887 0 0 0 2.235.616A4.928 4.928 0 0 1 1.67 3.148 13.98 13.98 0 0 0 11.82 8.292a4.929 4.929 0 0 1 8.39-4.49 9.868 9.868 0 0 0 3.128-1.196 4.941 4.941 0 0 1-2.165 2.724A9.828 9.828 0 0 0 24 4.555a10.019 10.019 0 0 1-2.457 2.549z"/></svg></a><!--]--></div><div class="VPFlyout VPNavBarExtra extra" data-v-57f83237 data-v-e5c8c6ca data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" aria-label="extra navigation" data-v-62bba1f9><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="icon" data-v-62bba1f9><circle cx="12" cy="12" r="2"></circle><circle cx="19" cy="12" r="2"></circle><circle cx="5" cy="12" r="2"></circle></svg></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><!----><!--[--><!--[--><!----><div class="group" data-v-e5c8c6ca><div class="item appearance" data-v-e5c8c6ca><p class="label" data-v-e5c8c6ca>Appearance</p><div class="appearance-action" data-v-e5c8c6ca><button class="VPSwitch VPSwitchAppearance" type="button" role="switch" title="toggle dark mode" aria-checked="false" data-v-e5c8c6ca data-v-65b67168 data-v-56eb52d1><span class="check" data-v-56eb52d1><span class="icon" data-v-56eb52d1><!--[--><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="sun" data-v-65b67168><path d="M12,18c-3.3,0-6-2.7-6-6s2.7-6,6-6s6,2.7,6,6S15.3,18,12,18zM12,8c-2.2,0-4,1.8-4,4c0,2.2,1.8,4,4,4c2.2,0,4-1.8,4-4C16,9.8,14.2,8,12,8z"></path><path d="M12,4c-0.6,0-1-0.4-1-1V1c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,3.6,12.6,4,12,4z"></path><path d="M12,24c-0.6,0-1-0.4-1-1v-2c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,23.6,12.6,24,12,24z"></path><path d="M5.6,6.6c-0.3,0-0.5-0.1-0.7-0.3L3.5,4.9c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C6.2,6.5,5.9,6.6,5.6,6.6z"></path><path d="M19.8,20.8c-0.3,0-0.5-0.1-0.7-0.3l-1.4-1.4c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C20.3,20.7,20,20.8,19.8,20.8z"></path><path d="M3,13H1c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S3.6,13,3,13z"></path><path d="M23,13h-2c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S23.6,13,23,13z"></path><path d="M4.2,20.8c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C4.7,20.7,4.5,20.8,4.2,20.8z"></path><path d="M18.4,6.6c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C18.9,6.5,18.6,6.6,18.4,6.6z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="moon" data-v-65b67168><path d="M12.1,22c-0.3,0-0.6,0-0.9,0c-5.5-0.5-9.5-5.4-9-10.9c0.4-4.8,4.2-8.6,9-9c0.4,0,0.8,0.2,1,0.5c0.2,0.3,0.2,0.8-0.1,1.1c-2,2.7-1.4,6.4,1.3,8.4c2.1,1.6,5,1.6,7.1,0c0.3-0.2,0.7-0.3,1.1-0.1c0.3,0.2,0.5,0.6,0.5,1c-0.2,2.7-1.5,5.1-3.6,6.8C16.6,21.2,14.4,22,12.1,22zM9.3,4.4c-2.9,1-5,3.6-5.2,6.8c-0.4,4.4,2.8,8.3,7.2,8.7c2.1,0.2,4.2-0.4,5.8-1.8c1.1-0.9,1.9-2.1,2.4-3.4c-2.5,0.9-5.3,0.5-7.5-1.1C9.2,11.4,8.1,7.7,9.3,4.4z"></path></svg><!--]--></span></span></button></div></div></div><div class="group" data-v-e5c8c6ca><div class="item social-links" data-v-e5c8c6ca><div class="VPSocialLinks social-links-list" data-v-e5c8c6ca data-v-8a65be56><!--[--><a class="VPSocialLink no-icon" href="https://github.com/andatoshiki" aria-label="github" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>GitHub</title><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"/></svg></a><a class="VPSocialLink no-icon" href="https://twitter.com/andatoshiki" aria-label="twitter" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>Twitter</title><path d="M21.543 7.104c.015.211.015.423.015.636 0 6.507-4.954 14.01-14.01 14.01v-.003A13.94 13.94 0 0 1 0 19.539a9.88 9.88 0 0 0 7.287-2.041 4.93 4.93 0 0 1-4.6-3.42 4.916 4.916 0 0 0 2.223-.084A4.926 4.926 0 0 1 .96 9.167v-.062a4.887 4.887 0 0 0 2.235.616A4.928 4.928 0 0 1 1.67 3.148 13.98 13.98 0 0 0 11.82 8.292a4.929 4.929 0 0 1 8.39-4.49 9.868 9.868 0 0 0 3.128-1.196 4.941 4.941 0 0 1-2.165 2.724A9.828 9.828 0 0 0 24 4.555a10.019 10.019 0 0 1-2.457 2.549z"/></svg></a><!--]--></div></div></div><!--]--><!--]--></div></div></div><!--[--><!--]--><button type="button" class="VPNavBarHamburger hamburger" aria-label="mobile navigation" aria-expanded="false" aria-controls="VPNavScreen" data-v-57f83237 data-v-f865e4ad><span class="container" data-v-f865e4ad><span class="top" data-v-f865e4ad></span><span class="middle" data-v-f865e4ad></span><span class="bottom" data-v-f865e4ad></span></span></button></div></div></div></div><!----></header><div class="VPLocalNav reached-top" data-v-f6284a77 data-v-a41c4a1c><button class="menu" aria-expanded="false" aria-controls="VPSidebarNav" data-v-a41c4a1c><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="menu-icon" data-v-a41c4a1c><path d="M17,11H3c-0.6,0-1-0.4-1-1s0.4-1,1-1h14c0.6,0,1,0.4,1,1S17.6,11,17,11z"></path><path d="M21,7H3C2.4,7,2,6.6,2,6s0.4-1,1-1h18c0.6,0,1,0.4,1,1S21.6,7,21,7z"></path><path d="M21,15H3c-0.6,0-1-0.4-1-1s0.4-1,1-1h18c0.6,0,1,0.4,1,1S21.6,15,21,15z"></path><path d="M17,19H3c-0.6,0-1-0.4-1-1s0.4-1,1-1h14c0.6,0,1,0.4,1,1S17.6,19,17,19z"></path></svg><span class="menu-text" data-v-a41c4a1c>Menu</span></button><div class="VPLocalNavOutlineDropdown" style="--vp-vh:0px;" data-v-a41c4a1c data-v-44ae7a43><button data-v-44ae7a43>Return to top</button><!----></div></div><aside class="VPSidebar" data-v-f6284a77 data-v-7ab77f34><div class="curtain" data-v-7ab77f34></div><nav class="nav" id="VPSidebarNav" aria-labelledby="sidebar-aria-label" tabindex="-1" data-v-7ab77f34><span class="visually-hidden" id="sidebar-aria-label" data-v-7ab77f34> Sidebar Navigation </span><!--[--><!--]--><!--[--><div class="group" data-v-7ab77f34><section class="VPSidebarItem level-0 collapsible has-active" data-v-7ab77f34 data-v-1b9f5c6f><div class="item" role="button" tabindex="0" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><h2 class="text" data-v-1b9f5c6f>IPhO Formulas: JP Ver.</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-1b9f5c6f><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="caret-icon" data-v-1b9f5c6f><path d="M9,19c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l5.3-5.3L8.3,6.7c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l6,6c0.4,0.4,0.4,1,0,1.4l-6,6C9.5,18.9,9.3,19,9,19z"></path></svg></div></div><div class="items" data-v-1b9f5c6f><!--[--><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/1" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>1: 数学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/2" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>2: 一般的な推奨事</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/3" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>3: 運動学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/4" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>4: 力学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/5" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>5: 振動と波</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/6" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>6: 幾何光学，測光</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/7" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>7: 波動光学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/8" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>8: 電気回路</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/9" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>9: 電磁気学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/10" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>10: 熱力</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/11" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>11: 量子力学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/12" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>12: Keplerの法則</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/13" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>13: 相対性理論</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><!--]--><!--[--><!--]--></nav></aside><div class="VPContent has-sidebar" id="VPContent" data-v-f6284a77 data-v-f3ed2c70><div class="VPDoc has-sidebar has-aside" data-v-f3ed2c70 data-v-39e6c32d><!--[--><!--]--><div class="container" data-v-39e6c32d><div class="aside" data-v-39e6c32d><div class="aside-curtain" data-v-39e6c32d></div><div class="aside-container" data-v-39e6c32d><div class="aside-content" data-v-39e6c32d><div class="VPDocAside" data-v-39e6c32d data-v-f5b3965e><!--[--><!--]--><!--[--><!--]--><div class="VPDocAsideOutline" role="navigation" data-v-f5b3965e data-v-99fa007f><div class="content" data-v-99fa007f><div class="outline-marker" data-v-99fa007f></div><div class="outline-title" role="heading" aria-level="2" data-v-99fa007f>TOC</div><nav aria-labelledby="doc-outline-aria-label" data-v-99fa007f><span class="visually-hidden" id="doc-outline-aria-label" data-v-99fa007f> Table of Contents for current page </span><ul class="root" data-v-99fa007f data-v-29e3fa2f><!--[--><!--]--></ul></nav></div></div><!--[--><!--]--><div class="spacer" data-v-f5b3965e></div><!--[--><!--]--><!----><!--[--><!--]--><!--[--><!--[--><!--[--><!--[--><div class="VPDocAsideSponsors"><div class="VPSponsors vp-sponsor aside"><!--[--><section class="vp-sponsor-section"><!----><div class="VPSponsorsGrid vp-sponsor-grid medium"><!--[--><div class="vp-sponsor-grid-item"><a class="vp-sponsor-grid-link" target="_blank" rel="sponsored noopener"><article class="vp-sponsor-grid-box"><h4 class="visually-hidden"></h4><img class="vp-sponsor-grid-image" src="https://jsd.toshiki.dev/gh/andatoshiki/toshiki-notebook@master/assets/logo/sponsor/telegram.png"></article></a></div><!--]--></div></section><!--]--></div></div><!--]--><!--]--><!--]--><!--]--></div></div></div></div><div class="content" data-v-39e6c32d><div class="content-container" data-v-39e6c32d><!--[--><!--]--><!----><main class="main" data-v-39e6c32d><div style="position:relative;" class="vp-doc _academic_physics_ipho-formulas-jpn_12" data-v-39e6c32d><div><h1 id="formulas-for-ipho-日本語版-section-12" tabindex="-1">Formulas for IPhO 日本語版: Section 12 <a class="header-anchor" href="#formulas-for-ipho-日本語版-section-12" aria-label="Permalink to "Formulas for IPhO 日本語版: Section 12""></a></h1><div><section class="border-b-1 border-[var(--vp-c-divider)] w-full border-b-solid mt-[24px] pb-[12px] flex gap-[12px] mb-[12px] flex-wrap max-w-[85%]"><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 16 16" width="1.2em" height="1.2em"><path fill="currentColor" d="M8 16A8 8 0 1 1 8 0a8 8 0 0 1 0 16Zm.847-8.145a2.502 2.502 0 1 0-1.694 0C5.471 8.261 4 9.775 4 11c0 .395.145.995 1 .995h6c.855 0 1-.6 1-.995c0-1.224-1.47-2.74-3.153-3.145Z"></path></svg> Author:<span>Anda Toshiki</span></div><!----><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 15 15" width="1.2em" height="1.2em"><path fill="currentColor" fill-rule="evenodd" d="M1.903 7.297c0 3.044 2.207 5.118 4.686 5.547a.521.521 0 1 1-.178 1.027C3.5 13.367.861 10.913.861 7.297c0-1.537.699-2.745 1.515-3.663c.585-.658 1.254-1.193 1.792-1.602H2.532a.5.5 0 0 1 0-1h3a.5.5 0 0 1 .5.5v3a.5.5 0 0 1-1 0V2.686l-.001.002c-.572.43-1.27.957-1.875 1.638c-.715.804-1.253 1.776-1.253 2.97Zm11.108.406c0-3.012-2.16-5.073-4.607-5.533a.521.521 0 1 1 .192-1.024c2.874.54 5.457 2.98 5.457 6.557c0 1.537-.699 2.744-1.515 3.663c-.585.658-1.254 1.193-1.792 1.602h1.636a.5.5 0 1 1 0 1h-3a.5.5 0 0 1-.5-.5v-3a.5.5 0 1 1 1 0v1.845h.002c.571-.432 1.27-.958 1.874-1.64c.715-.803 1.253-1.775 1.253-2.97Z" clip-rule="evenodd"></path></svg> Updated:<span>2 minutes ago</span></div><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 16 16" width="1.2em" height="1.2em"><path fill="currentColor" d="M9.293 0H4a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h8a2 2 0 0 0 2-2V4.707A1 1 0 0 0 13.707 4L10 .293A1 1 0 0 0 9.293 0zM9.5 3.5v-2l3 3h-2a1 1 0 0 1-1-1zM5.485 6.879l1.036 4.144l.997-3.655a.5.5 0 0 1 .964 0l.997 3.655l1.036-4.144a.5.5 0 0 1 .97.242l-1.5 6a.5.5 0 0 1-.967.01L8 9.402l-1.018 3.73a.5.5 0 0 1-.967-.01l-1.5-6a.5.5 0 1 1 .97-.242z"></path></svg> Words:<span>332</span></div><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 20 20" width="1.2em" height="1.2em"><path fill="currentColor" d="M10 0a10 10 0 1 0 10 10A10 10 0 0 0 10 0zm2.5 14.5L9 11V4h2v6l3 3z"></path></svg> Reading:<span>1 min</span></div></section></div><h2 id="_12-kepler-の法則" tabindex="-1">12: Kepler の法則 <a class="header-anchor" href="#_12-kepler-の法則" aria-label="Permalink to "12: Kepler の法則""></a></h2><h3 id="_12-1-f-u" tabindex="-1">12.1: F & U <a class="header-anchor" href="#_12-1-f-u" aria-label="Permalink to "12.1: F & U""></a></h3><ol><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo>=</mo><mi>G</mi><mi>M</mi><mi>m</mi><mi mathvariant="normal">/</mi><msup><mi>r</mi><mn>2</mn></msup><mo separator="true">,</mo><mi>U</mi><mo>=</mo><mo>−</mo><mi>G</mi><mi>M</mi><mi>m</mi><mi mathvariant="normal">/</mi><mi>r</mi><mtext>. </mtext></mrow><annotation encoding="application/x-tex">F=G M m / r^2, U=-G M m / r \text {. }</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">GM</span><span class="mord mathnormal">m</span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.10903em;">GM</span><span class="mord mathnormal">m</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord text"><span class="mord">. </span></span></span></span></span></li></ol><h3 id="_12-2-kepler-の第一法則" tabindex="-1">12.2: Kepler の第一法則 <a class="header-anchor" href="#_12-2-kepler-の第一法則" aria-label="Permalink to "12.2: Kepler の第一法則""></a></h3><ol start="2"><li>Kepler の第一法則 (2 質点の重力相互作用)：それぞ れの軌道は，系の質量中心に焦点を持つ楕円，双曲線, 放物線になる. これは Runge-Lenz ベクトルから得ら れる (ポイント 9).</li></ol><h3 id="_12-3-kepler-の第二法則" tabindex="-1">12.3: Kepler の第二法則 <a class="header-anchor" href="#_12-3-kepler-の第二法則" aria-label="Permalink to "12.3: Kepler の第二法則""></a></h3><ol start="3"><li>Kepler の第二法則（角運動量の保存）: 中心力が働く 場にある質点について，その位置ベクトルは単位時間 に一定の面積を描く.</li></ol><h3 id="_12-4-kepler-の第三法則" tabindex="-1">12.4: Kepler の第三法則 <a class="header-anchor" href="#_12-4-kepler-の第三法則" aria-label="Permalink to "12.4: Kepler の第三法則""></a></h3><ol start="4"><li>Kepler の第三法則 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>:</mo><msup><mi>r</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex">: r^{-2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span> に比例する力が働く場で楕円 軌道を描く複数の質点について, 周期は長半径の <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{3}{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span> 乗 に比例する :<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msubsup><mi>T</mi><mn>1</mn><mn>2</mn></msubsup><mi mathvariant="normal">/</mi><msubsup><mi>T</mi><mn>2</mn><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>a</mi><mn>1</mn><mn>3</mn></msubsup><mi mathvariant="normal">/</mi><msubsup><mi>a</mi><mn>2</mn><mn>3</mn></msubsup></mrow><annotation encoding="application/x-tex">T_1^2 / T_2^2=a_1^3 / a_2^3 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1141em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1141em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span></span></span></span></p></li></ol><h3 id="_12-5-楕円軌道" tabindex="-1">12.5: 楕円軌道 <a class="header-anchor" href="#_12-5-楕円軌道" aria-label="Permalink to "12.5: 楕円軌道""></a></h3><ol start="5"><li>重力場中で楕円軌道を描く質点の全エネルギー <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>K</mi><mo>+</mo><mi>U</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(K+U)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mclose">)</span></span></span></span> :<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>E</mi><mo>=</mo><mo>−</mo><mi>G</mi><mi>M</mi><mi>m</mi><mi mathvariant="normal">/</mi><mn>2</mn><mi>a</mi></mrow><annotation encoding="application/x-tex">E=-G M m / 2 a </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.10903em;">GM</span><span class="mord mathnormal">m</span><span class="mord">/2</span><span class="mord mathnormal">a</span></span></span></span></span></p></li></ol><h3 id="_12-6-楕円率" tabindex="-1">12.6: 楕円率 <a class="header-anchor" href="#_12-6-楕円率" aria-label="Permalink to "12.6: 楕円率""></a></h3><ol><li>楕円率が <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi><mo>=</mo><mi>d</mi><mi mathvariant="normal">/</mi><mi>a</mi><mo>≪</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\varepsilon=d / a \ll 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">ε</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">d</span><span class="mord">/</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≪</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> の場合, 軌道は焦点をずらし た円形をしていると考えられる.</li></ol><h3 id="_12-7-楕円の性質" tabindex="-1">12.7: 楕円の性質 <a class="header-anchor" href="#_12-7-楕円の性質" aria-label="Permalink to "12.7: 楕円の性質""></a></h3><ol start="2"><li>楕円の性質 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>:</mo><msub><mi>l</mi><mn>1</mn></msub><mo>+</mo><msub><mi>l</mi><mn>2</mn></msub><mo>=</mo><mn>2</mn><mi>a</mi><mtext>（</mtext><msub><mi>l</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">: l_1+l_2=2 a （ l_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord">2</span><span class="mord mathnormal">a</span><span class="mord cjk_fallback">（</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> と <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">l_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> は焦点までの距 離). <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>α</mi><mn>1</mn></msub><mo>=</mo><msub><mi>α</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\alpha_1=\alpha_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> (一方の焦点から出た光は他方の焦点に 反射する). <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mo>=</mo><mi>π</mi><mi>a</mi><mi>b</mi></mrow><annotation encoding="application/x-tex">S=\pi a b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">πab</span></span></span></span>.</li></ol><h3 id="_12-8-円の中心" tabindex="-1">12.8: 円の中心 <a class="header-anchor" href="#_12-8-円の中心" aria-label="Permalink to "12.8: 円の中心""></a></h3><ol start="3"><li>円とその円の中心に焦点をもつ楕円は長軸の部分での み接する.</li></ol><h3 id="_12-9-nge-lenz-ベクトル" tabindex="-1">12.9: nge-Lenz ベクトル <!----> <a class="header-anchor" href="#_12-9-nge-lenz-ベクトル" aria-label="Permalink to "12.9: nge-Lenz ベクトル <Badge type="tip" text="supplemental" />""></a></h3><ol start="4"><li>Runge-Lenz ベクトル（楕円率ベクトル）[訳者注：こ のベクトルはむしろ離心率と関係する.そこでここで は離心率ベクトルとして知られるベクトルを代わりに 記す.これは焦点から近日点に向かう向きで，大きさ が離心率 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>e</mi></mrow><annotation encoding="application/x-tex">e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">e</span></span></span></span> に一致する.]：<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="bold-italic">e</mi><mo>=</mo><mfrac><mrow><mi mathvariant="bold-italic">v</mi><mo>×</mo><mi mathvariant="bold-italic">M</mi></mrow><mrow><mi>G</mi><mi>M</mi><mi>m</mi></mrow></mfrac><mo>−</mo><msub><mi mathvariant="bold-italic">e</mi><mi>r</mi></msub><mo>=</mo><mtext> const. </mtext></mrow><annotation encoding="application/x-tex">\boldsymbol{e}=\frac{\boldsymbol{v} \times \boldsymbol{M}}{G M m}-\boldsymbol{e}_r=\text { const. } </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4444em;"></span><span class="mord"><span class="mord"><span class="mord boldsymbol">e</span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0491em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3631em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">GM</span><span class="mord mathnormal">m</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:0.03704em;">v</span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:0.11424em;">M</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5944em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord boldsymbol">e</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord text"><span class="mord"> const. </span></span></span></span></span></span></p></li></ol></div></div></main><footer class="VPDocFooter" data-v-39e6c32d data-v-bae355c8><!--[--><!--[--><!--[--><!--[--><!----><!--]--><!--]--><!--]--><!--]--><div class="edit-info" data-v-bae355c8><div class="edit-link" data-v-bae355c8><a class="VPLink link vp-external-link-icon no-icon edit-link-button" href="https://github.com/andatoshiki/toshiki-notebook/edit/master/docs/academic/physics/ipho-formulas-jpn/12.md" target="_blank" rel="noreferrer" data-v-bae355c8><!--[--><svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 24 24" class="edit-link-icon" aria-label="edit icon" data-v-bae355c8><path d="M18,23H4c-1.7,0-3-1.3-3-3V6c0-1.7,1.3-3,3-3h7c0.6,0,1,0.4,1,1s-0.4,1-1,1H4C3.4,5,3,5.4,3,6v14c0,0.6,0.4,1,1,1h14c0.6,0,1-0.4,1-1v-7c0-0.6,0.4-1,1-1s1,0.4,1,1v7C21,21.7,19.7,23,18,23z"></path><path d="M8,17c-0.3,0-0.5-0.1-0.7-0.3C7,16.5,6.9,16.1,7,15.8l1-4c0-0.2,0.1-0.3,0.3-0.5l9.5-9.5c1.2-1.2,3.2-1.2,4.4,0c1.2,1.2,1.2,3.2,0,4.4l-9.5,9.5c-0.1,0.1-0.3,0.2-0.5,0.3l-4,1C8.2,17,8.1,17,8,17zM9.9,12.5l-0.5,2.1l2.1-0.5l9.3-9.3c0.4-0.4,0.4-1.1,0-1.6c-0.4-0.4-1.2-0.4-1.6,0l0,0L9.9,12.5z M18.5,2.5L18.5,2.5L18.5,2.5z"></path></svg> Edit this page on GitHub<!--]--></a></div><div class="last-updated" data-v-bae355c8><p class="VPLastUpdated" data-v-bae355c8 data-v-ec8405ef>Last updated: <time datetime="2023-09-17T09:19:21.000Z" data-v-ec8405ef></time></p></div></div><nav class="prev-next" data-v-bae355c8><div class="pager" data-v-bae355c8><a class="pager-link prev" href="/academic/physics/ipho-formulas-jpn/11" data-v-bae355c8><span class="desc" data-v-bae355c8>Previous page</span><span class="title" data-v-bae355c8>11: 量子力学</span></a></div><div class="pager" data-v-bae355c8><a class="pager-link next" href="/academic/physics/ipho-formulas-jpn/13" data-v-bae355c8><span class="desc" data-v-bae355c8>Next page</span><span class="title" data-v-bae355c8>13: 相対性理論</span></a></div></nav></footer><!--[--><!--[--><!--[--><div id="comment-container"></div><!--]--><!--]--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter has-sidebar" data-v-f6284a77 data-v-b69a1592><div class="container" data-v-b69a1592><p class="message" data-v-b69a1592>Wrote with <i class="heart fa fa-heart fa-xs fa-beat"></i> and <i class="coffee fa fa-coffee fa-xs" aria-hidden="true"></i> by <a href="https://toshiki.dev">Anda Toshiki</a> at <code>root@andatoshiki:/~</code></p><p class="copyright" data-v-b69a1592>Copyright © 2023-2023 <a href="https://github.com/andatoshiki">Anda Toshiki</a>, <a href="https://github.com/lolilab">LoliLab</a> and <a href="https://github.com/toshikidev">Toshiki Dev</a> present <br /><span id="siteruntime_span"></span></p></div></footer><!--[--><!--]--></div></div>
|
||
<script>window.__VP_HASH_MAP__=JSON.parse("{\"academic_chemistry_index.md\":\"9a99d374\",\"academic_chemistry_notes_12-5.md\":\"8f7737a4\",\"academic_physics_ipho-formulas-jpn_12.md\":\"97cf4aa6\",\"academic_physics_ipho-formulas-jpn_2.md\":\"a4fe4b30\",\"academic_physics_index.md\":\"4851fd32\",\"academic_literature_writing_methods-of-development.md\":\"08089cb6\",\"academic_literature_index.md\":\"d662bbd6\",\"academic_physics_ipho-formulas-jpn_11.md\":\"fbf2126f\",\"academic_chemistry_problems_03-02-2.md\":\"b1934117\",\"academic_chemistry_problems_03-02-3.md\":\"dbcfad8b\",\"academic_physics_ipho-formulas-jpn_10.md\":\"9ec8a936\",\"academic_chemistry_problems_02-20.md\":\"da62657a\",\"academic_physics_ipho-formulas-jpn_3.md\":\"e2a77865\",\"academic_physics_ipho-formulas-jpn_13.md\":\"d4993a10\",\"academic_chemistry_problems_03-02-1.md\":\"1d1baaca\",\"development_aws_license.md\":\"815a0852\",\"development_aws_scientific-computing.md\":\"d3ec5923\",\"development_aws_serverless.md\":\"d3e28778\",\"development_aws_webserver.md\":\"99c6e9c3\",\"development_file-naming-convention.md\":\"d1ace5ab\",\"development_rclone-for-r2.md\":\"8b91a94d\",\"getting-started.md\":\"4b1628bc\",\"jp_index.md\":\"9372a59e\",\"roadmap.md\":\"a9a962a5\",\"save_reading_index.md\":\"a209f5a8\",\"save_reading_outliers_2.md\":\"e74f9888\",\"save_reading_outliers_3.md\":\"7c8a8fc2\",\"save_reading_outliers_4.md\":\"1234a2d9\",\"academic_physics_ipho-formulas-jpn_4.md\":\"3a8c99c7\",\"academic_vocabulary_2023_02_2023-02-27.md\":\"af6b808b\",\"academic_vocabulary_index.md\":\"d740c703\",\"application_markdown-it-katex_how-to-use.md\":\"e02b37e0\",\"application_markdown-it-katex_tips.md\":\"bda1e594\",\"application_vitepress-plugin-shiki-twoslash_api_annotations.md\":\"1b7732d0\",\"application_vitepress-plugin-shiki-twoslash_api_cutting.md\":\"347c0da3\",\"application_vitepress-plugin-shiki-twoslash_api_emit.md\":\"528ab068\",\"application_vitepress-plugin-shiki-twoslash_api_errors.md\":\"988ae844\",\"application_vitepress-plugin-shiki-twoslash_api_includes.md\":\"5ae0055a\",\"application_vitepress-plugin-shiki-twoslash_api_logging.md\":\"32122f74\",\"application_vitepress-plugin-shiki-twoslash_config_flags.md\":\"86416600\",\"application_vitepress-plugin-shiki-twoslash_config_reference.md\":\"ca3b2147\",\"application_vitepress-plugin-shiki-twoslash_guide_custom-theme.md\":\"f140cb9f\",\"application_vitepress-plugin-shiki-twoslash_guide_markdown-extensions.md\":\"a30fc0c6\",\"application_vitepress-plugin-shiki-twoslash_index.md\":\"1471d1a6\",\"development_aws_acknowledgement.md\":\"d5010f77\",\"development_aws_appendix.md\":\"5190c057\",\"development_aws_assignments.md\":\"3f007692\",\"development_aws_author.md\":\"4fd5d4be\",\"save_reading_outliers_1.md\":\"9ed27027\",\"development_aws_aws-batch.md\":\"27130560\",\"development_aws_aws-get-started.md\":\"e74f8c76\",\"development_aws_cloud.md\":\"451c3969\",\"development_aws_docker-system.md\":\"e2d182fa\",\"academic_physics_ipho-formulas-jpn_1.md\":\"db3180dc\",\"development_aws_handson-bashoutter.md\":\"47c1cc1e\",\"development_aws_handson-ec2.md\":\"9163183b\",\"academic_physics_ipho-formulas-jpn_7.md\":\"36e5f9b6\",\"application_vitepress-plugin-shiki-twoslash_api_queries.md\":\"12a832bd\",\"development_aws_handson-jupyter.md\":\"6b27c06d\",\"application_vitepress-plugin-shiki-twoslash_api_types.md\":\"074f3432\",\"index.md\":\"88e57263\",\"development_aws_handson-serverless.md\":\"c2d673af\",\"javascript_notes_1_1-1.md\":\"ddd00ea9\",\"development_aws_index.md\":\"6de28b36\",\"application_vitepress-plugin-shiki-twoslash_api_multi-file.md\":\"9c91d5c2\",\"academic_physics_ipho-formulas-jpn_6.md\":\"7b7245c7\",\"development_aws_closing.md\":\"7de486ec\",\"development_aws_handson-qabot.md\":\"959ea871\",\"javascript_notes_1_1-2.md\":\"638bf6b2\",\"academic_physics_ipho-formulas-jpn_5.md\":\"9b9c7eb1\",\"academic_physics_ipho-formulas-jpn_8.md\":\"02b6cabd\",\"development_aws_main.md\":\"b709a2eb\",\"academic_physics_ipho-formulas-jpn_9.md\":\"4c07ff1e\",\"application_markdown-it-katex_support-table.md\":\"58146274\",\"application_markdown-it-katex_support-function.md\":\"cb273b62\"}");window.__VP_SITE_DATA__=JSON.parse("{\"lang\":\"en-US\",\"dir\":\"ltr\",\"title\":\"Toshiki's Note\",\"description\":\"Toshiki's web notebook served via Vitepress!\",\"base\":\"/\",\"head\":[],\"appearance\":true,\"themeConfig\":{\"nav\":[{\"text\":\"Development\",\"link\":\"/development/\"},{\"text\":\"Academic\",\"items\":[{\"text\":\"K-12\",\"items\":[{\"text\":\"Chemistry\",\"link\":\"/academic/chemistry/index\",\"activeMatch\":\"/academic/chemistry/\"},{\"text\":\"Discrete Math.\",\"link\":\"/discrete-math/index\",\"activeMatch\":\"/categories/fragments/\"},{\"text\":\"Literature\",\"link\":\"/academic/literature/index\",\"activeMatch\":\"/academic/literature/\"}]},{\"text\":\"Tools\",\"items\":[{\"text\":\"Formulas for IPhO JPN.\",\"link\":\"/academic/physics/ipho-formulas-jpn/1\",\"activeMatch\":\"/academic/physics/ipho-formulas-jpn/\"}]},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"}],\"activeMatch\":\"/academic/\"},{\"text\":\"Application\",\"items\":[{\"text\":\"Personal projects\",\"items\":[{\"text\":\"markdown-it-katex\",\"link\":\"/application/markdown-it-katex/how-to-use\",\"activeMatch\":\"/application/markdown-it-katex/\"},{\"text\":\"vitepress-plugin-shiki-twoslash\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/index\",\"activeMatch\":\"/application/vitepress-plugin-shiki-twoslash/index\"}]}],\"activeMatch\":\"/save/\"},{\"text\":\"Save\",\"items\":[{\"text\":\"Reading\",\"link\":\"/save/reading/index\",\"activeMatch\":\"/save/reading/\"},{\"text\":\"Vocabulary\",\"link\":\"/academic/vocabulary/index\",\"activeMatch\":\"/academic/vocabulary/\"}],\"activeMatch\":\"/save/\"}],\"sidebar\":{\"/development/\":[{\"text\":\"Notes & Issues\",\"collapsed\":false,\"items\":[{\"text\":\"File Naming Convention\",\"link\":\"/development/file-naming-convention\"},{\"text\":\"RClone for R2\",\"link\":\"/development/rclone-for-r2\"}]},{\"text\":\"コードで学ぶAWS入門\",\"collapsed\":false,\"items\":[{\"text\":\"背景\",\"link\":\"/development/aws/index\"},{\"text\":\"はじめに！\",\"link\":\"/development/aws/main\"},{\"text\":\"クラウド概論\",\"link\":\"/development/aws/cloud.md\"},{\"text\":\"AWS 入門\",\"link\":\"/development/aws/aws-get-started\"},{\"text\":\"Hands-on 1: 初めての EC2 インスタンスを起動する\",\"link\":\"/development/aws/handson-ec2.md\"},{\"text\":\"クラウドで行う科学計算・機械学習\",\"link\":\"/development/aws/scientific-computing.md\"},{\"text\":\"Hands-on 2: AWS でディープラーニングを実践\",\"link\":\"/development/aws/handson-ec2.md\"},{\"text\":\"Docker 入門\",\"link\":\"/development/aws/docker-system\"},{\"text\":\"Hands-on 3: AWS で自動質問回答ボットを走らせる\",\"link\":\"/development/aws/handson-qabot\"},{\"text\":\"Hands-on 4: AWS Batch を使って機械学習のハイパーパラメータサーチを並列化する\",\"link\":\"/development/aws/aws-batch\"},{\"text\":\"Web サービスの作り方\",\"link\":\"/development/aws/webserver\"},{\"text\":\"Serverless architecture\",\"link\":\"/development/aws/serverless\"},{\"text\":\"Hands-on 5: サーバーレス入門\",\"link\":\"/development/aws/handson-serverless\"},{\"text\":\"Hands-on 6: Bashoutter\",\"link\":\"/development/aws/handson-bashoutter\"},{\"text\":\"まとめ\",\"link\":\"/development/aws/closing\"},{\"text\":\"ppendix: 環境構築\",\"link\":\"/development/aws/appendix\"},{\"text\":\"謝辞\",\"link\":\"/development/aws/acknowledgement\"}]}],\"/academic/chemistry/\":[{\"text\":\"Textbook\",\"collapsed\":true,\"items\":[{\"text\":\"12-5: Reaction Mechanism\",\"link\":\"/academic/chemistry/notes/12-5\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"}]},{\"text\":\"Kinetics\",\"collapsed\":false,\"items\":[{\"text\":\"Rate determining steps\",\"link\":\"/academic/chemistry/notes/kinetics/rate-determining-step\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"}]},{\"text\":\"Problems & Solutions\",\"collapsed\":true,\"items\":[{\"text\":\"Problem: 02-20\",\"link\":\"/academic/chemistry/problems/02-20\"},{\"text\":\"Problem: 03-02-1\",\"link\":\"/academic/chemistry/problems/03-02-1\"},{\"text\":\"Problem: 03-02-2\",\"link\":\"/academic/chemistry/problems/03-02-2\"},{\"text\":\"Problem: 03-02-3\",\"link\":\"/academic/chemistry/problems/03-02-3\"}]}],\"/academic/physics\":[{\"text\":\"IPhO Formulas: JP Ver.\",\"collapsed\":false,\"items\":[{\"text\":\"1: 数学\",\"link\":\"/academic/physics/ipho-formulas-jpn/1\"},{\"text\":\"2: 一般的な推奨事\",\"link\":\"/academic/physics/ipho-formulas-jpn/2\"},{\"text\":\"3: 運動学\",\"link\":\"/academic/physics/ipho-formulas-jpn/3\"},{\"text\":\"4: 力学\",\"link\":\"/academic/physics/ipho-formulas-jpn/4\"},{\"text\":\"5: 振動と波\",\"link\":\"/academic/physics/ipho-formulas-jpn/5\"},{\"text\":\"6: 幾何光学，測光\",\"link\":\"/academic/physics/ipho-formulas-jpn/6\"},{\"text\":\"7: 波動光学\",\"link\":\"/academic/physics/ipho-formulas-jpn/7\"},{\"text\":\"8: 電気回路\",\"link\":\"/academic/physics/ipho-formulas-jpn/8\"},{\"text\":\"9: 電磁気学\",\"link\":\"/academic/physics/ipho-formulas-jpn/9\"},{\"text\":\"10: 熱力\",\"link\":\"/academic/physics/ipho-formulas-jpn/10\"},{\"text\":\"11: 量子力学\",\"link\":\"/academic/physics/ipho-formulas-jpn/11\"},{\"text\":\"12: Keplerの法則\",\"link\":\"/academic/physics/ipho-formulas-jpn/12\"},{\"text\":\"13: 相対性理論\",\"link\":\"/academic/physics/ipho-formulas-jpn/13\"}]}],\"/academic/vocabulary/\":[{\"text\":\"Vocabulary\",\"collapsed\":true,\"items\":[{\"text\":\"2023-02-27\",\"link\":\"/academic/vocabulary/2023/02/2023-02-27\"}]}],\"/academic/literature/\":[{\"text\":\"Writing Resources\",\"collapsed\":true,\"items\":[{\"text\":\"Patterns of Organization and Methods of Development\",\"link\":\"/academic/literature/writing/methods-of-development\"}]}],\"/javascript/\":[{\"text\":\"1: Basic JavaScript-Value, Variables, and Control Flow\",\"collapsed\":true,\"items\":[{\"text\":\"1-1: Numbers\",\"link\":\"/javascript/notes/1/1-1\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"}]}],\"/save/reading/\":[{\"text\":\"Outliers\",\"collapsed\":true,\"items\":[{\"text\":\"Introduction & Chapter 1: The Roseto Mystery\",\"link\":\"/save/reading/outliers/1\"},{\"text\":\"Chapter 2: The 10,000-Hour Rule\",\"link\":\"/save/reading/outliers/2\"},{\"text\":\"Chapter 3: The Trouble with Geniuses, Part 1\",\"link\":\"/save/reading/outliers/3\"},{\"text\":\"Chapter 4: The Trouble with Geniuses, Part 2\",\"link\":\"/save/reading/outliers/4\"}]}],\"/application/markdown-it-katex/\":[{\"text\":\"markdown-it-katex\",\"collapsed\":false,\"items\":[{\"text\":\"1: How to use?\",\"link\":\"/application/markdown-it-katex/how-to-use\"},{\"text\":\"2: KaTeX supported functions\",\"link\":\"/application/markdown-it-katex/support-function\"},{\"text\":\"3: KaTeX support tables\",\"link\":\"/application/markdown-it-katex/support-table\"},{\"text\":\"4: Tips\",\"link\":\"/application/markdown-it-katex/tips\"}]}],\"/application/vitepress-plugin-shiki-twoslash/\":[{\"text\":\"Guide\",\"collapsed\":false,\"items\":[{\"text\":\"Getting Started\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/\"},{\"text\":\"Markdown Extensions\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/guide/markdown-extensions\"},{\"text\":\"Using a Custom Theme\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/guide/custom-theme\"}]},{\"text\":\"Features\",\"collapsed\":false,\"items\":[{\"text\":\"Queries\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/queries\"},{\"text\":\"Errors\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/errors\"},{\"text\":\"Emit\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/emit\"},{\"text\":\"Cutting\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/cutting\"},{\"text\":\"Multi-file\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/multi-file\"},{\"text\":\"@types\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/types\"},{\"text\":\"Meta Annotations\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/annotations\"},{\"text\":\"Logging\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/logging\"},{\"text\":\"Includes\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/includes\"}]},{\"text\":\"Config\",\"collapsed\":false,\"items\":[{\"text\":\"Reference\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/config/reference\"},{\"text\":\"Compiler Flags\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/config/flags\"}]}]},\"footer\":{\"copyright\":\"Copyright © 2023-2023 <a href=\\\"https://github.com/andatoshiki\\\">Anda Toshiki</a>, <a href=\\\"https://github.com/lolilab\\\">LoliLab</a> and <a href=\\\"https://github.com/toshikidev\\\">Toshiki Dev</a> present <br /><span id=\\\"siteruntime_span\\\"></span>\",\"message\":\"Wrote with <i class=\\\"heart fa fa-heart fa-xs fa-beat\\\"></i> and <i class=\\\"coffee fa fa-coffee fa-xs\\\" aria-hidden=\\\"true\\\"></i> by <a href=\\\"https://toshiki.dev\\\">Anda Toshiki</a> at <code>root@andatoshiki:/~</code>\"},\"logo\":\"/logos/logo.png\",\"outline\":\"deep\",\"outlineTitle\":\"TOC\",\"outlineBadges\":false,\"lastUpdatedText\":\"Last updated\",\"algolia\":{\"appId\":\"G9IUR45K98\",\"apiKey\":\"8528cc91281d8112b28f508317a96dd3\",\"indexName\":\"toshiki-notebook\"},\"editLink\":{\"pattern\":\"https://github.com/andatoshiki/toshiki-notebook/edit/master/docs/:path\",\"text\":\"Edit this page on GitHub\"},\"socialLinks\":[{\"icon\":\"github\",\"link\":\"https://github.com/andatoshiki\"},{\"icon\":\"twitter\",\"link\":\"https://twitter.com/andatoshiki\"}]},\"locales\":{\"/\":{\"label\":\"English\",\"lang\":\"en-US\"},\"/jp/\":{\"label\":\"Japanese\",\"title\":\"Vue Test Utils\",\"lang\":\"jp-JP\",\"description\":\"La documentation officielle de Vue Test Utils\"}},\"scrollOffset\":90,\"cleanUrls\":true}");</script>
|
||
|
||
</body>
|
||
</html> |