[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki9\/archives\/285371#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki9\/archives\/285371","headline":"\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5 – Wikipedia","name":"\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5 – Wikipedia","description":"before-content-x4 \u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306f\u3001\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u7a4d\u5206\u6cd5 (\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5) \u306e\u4e00\u7a2e\u30012\u6b21\u306e\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u6570\u5024\u7a4d\u5206\u6cd5\u3067\u3042\u308b[1]\u3002\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306f\u3001 x\u00a8=d2xdt2=F(x){displaystyle {ddot {x}}={frac {d^{2}x}{dt^{2}}}=F(x)} after-content-x4 \u307e\u305f\u306f after-content-x4 v\u02d9=dvdt=F(x),x\u02d9=dxdt=v{displaystyle {dot {v}}={frac {dv}{dt}}=F(x),quad {dot {x}}={frac {dx}{dt}}=v} \u3068\u3044\u3046\u5f62\u5f0f\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u969b\u306b\u7528\u3044\u3089\u308c\u3001\u7279\u306b\u3001\u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u529b\u5b66\u7cfb\u306e\u8a08\u7b97\u3067\u91cd\u8981\u3067\u3042\u308b\u3002 \u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306b\u304a\u3051\u308b\u6642\u9593\u7a4d\u5206\u306f\u3001\u4e92\u3044\u306e\u4e0a\u3092\u86d9\u8df3\u3073","datePublished":"2022-04-24","dateModified":"2022-04-24","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki9\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki9\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/04687548686eca61ae890949790b0240b94a0894","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/04687548686eca61ae890949790b0240b94a0894","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki9\/archives\/285371","about":["Wiki"],"wordCount":3246,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306f\u3001\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u7a4d\u5206\u6cd5 (\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5) \u306e\u4e00\u7a2e\u30012\u6b21\u306e\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u6570\u5024\u7a4d\u5206\u6cd5\u3067\u3042\u308b[1]\u3002\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306f\u3001x\u00a8=d2xdt2=F(x){displaystyle {ddot {x}}={frac {d^{2}x}{dt^{2}}}=F(x)}       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u307e\u305f\u306f       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4v\u02d9=dvdt=F(x),x\u02d9=dxdt=v{displaystyle {dot {v}}={frac {dv}{dt}}=F(x),quad {dot {x}}={frac {dx}{dt}}=v}\u3068\u3044\u3046\u5f62\u5f0f\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u969b\u306b\u7528\u3044\u3089\u308c\u3001\u7279\u306b\u3001\u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u529b\u5b66\u7cfb\u306e\u8a08\u7b97\u3067\u91cd\u8981\u3067\u3042\u308b\u3002\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306b\u304a\u3051\u308b\u6642\u9593\u7a4d\u5206\u306f\u3001\u4e92\u3044\u306e\u4e0a\u3092\u86d9\u8df3\u3073 (Leap-frog) \u3059\u308b\u3088\u3046\u306b\u4f4d\u7f6e x(t){displaystyle x(t)} \u3068\u901f\u5ea6 v(t)=x\u02d9(t){displaystyle v(t)={dot {x}}(t)} \u3092\u305a\u3089\u3057\u3066\u6642\u9593\u767a\u5c55\u3055\u305b\u308b\u306e\u304c\u7279\u5fb4\u3067\u3042\u308b\u3002\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306f\u3001\u30aa\u30a4\u30e9\u30fc\u6cd5\u304c\u4e00\u6b21\u7cbe\u5ea6\u3067\u3042\u308b\u306e\u3068\u306f\u5bfe\u7167\u7684\u306b\u3001\u4e8c\u6b21\u7cbe\u5ea6\u306e\u6570\u5024\u7a4d\u5206\u6cd5\u3067\u3042\u308b\u3002\u307e\u305f\u3001\u30aa\u30a4\u30e9\u30fc\u6cd5\u3068\u306f\u7570\u306a\u308a\u3001\u6642\u9593\u5e45\u304c\u5b9a\u6570        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u0394t{displaystyle Delta t} \u3067\u3042\u308a\u306a\u304a\u304b\u3064 \u0394t\u22642\/\u03c9{displaystyle Delta tleq 2\/omega } \u306a\u308b\u5468\u671f\u904b\u52d5\u3067\u5b89\u5b9a\u3068\u306a\u308b[2]\u3002\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u4f4d\u7f6e\u3068\u901f\u5ea6\u3092\u66f4\u65b0\u3059\u308b\u3002xi=xi\u22121+vi\u22121\/2\u0394t,ai=F(xi),vi+1\/2=vi\u22121\/2+ai\u0394t.{displaystyle {begin{aligned}x_{i}&=x_{i-1}+v_{i-1\/2}Delta t,\\a_{i}&=F(x_{i}),\\v_{i+1\/2}&=v_{i-1\/2}+a_{i}Delta t.end{aligned}}}\u3053\u3053\u3067\u3001xi{displaystyle x_{i}} \u306f i{displaystyle i} \u30b9\u30c6\u30c3\u30d7\u76ee\u3067\u306e\u4f4d\u7f6e\u3067\u3001vi+1\/2{displaystyle v_{i+1\/2}} \u306f i+1\/2{displaystyle i+1\/2} \u30b9\u30c6\u30c3\u30d7\u76ee\u306e\u901f\u5ea6\u3001ai{displaystyle a_{i}} \u306f i{displaystyle i} \u30b9\u30c6\u30c3\u30d7\u76ee\u306e\u52a0\u901f\u5ea6\u3067\u3042\u308b\u3002\u0394t{displaystyle Delta t} \u306f\u6642\u9593\u30b9\u30c6\u30c3\u30d7\u306e\u5927\u304d\u3055\u3067\u3042\u308b\u3002\u3053\u308c\u3089\u306e\u5f0f\u306f\u3001\u534a\u6574\u6570\u30b9\u30c6\u30c3\u30d7\u3092\u6d88\u53bb\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6574\u6570\u30b9\u30c6\u30c3\u30d7\u306e\u307f\u306e\u5f0f\u3067\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b[3]\u3002xi+1=xi+vi\u0394t+12ai\u0394t2,vi+1=vi+12(ai+ai+1)\u0394t.{displaystyle {begin{aligned}x_{i+1}&=x_{i}+v_{i}Delta t+{frac {1}{2}}a_{i}Delta t^{2},\\v_{i+1}&=v_{i}+{frac {1}{2}}(a_{i}+a_{i+1})Delta t.end{aligned}}}\u305f\u3060\u3057\u3001\u3053\u306e\u5f62\u5f0f\u3067\u306f\u3001\u6642\u9593\u30b9\u30c6\u30c3\u30d7 \u0394t{displaystyle Delta t} \u304c\u4e00\u5b9a\u5024\u3067\u306a\u3044\u9650\u308a\u5b89\u5b9a\u3067\u306f\u306a\u3044[4]\u3002\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306f\u3001\u52a0\u901f\u5ea6\u304c\u901f\u5ea6\u306b\u975e\u4f9d\u5b58\u3067\u3042\u308b\u3001\u91cd\u529b\u8a08\u7b97\u306b\u7528\u3044\u3089\u308c\u308b\u3053\u3068\u304c\u591a\u3044[5]\u3002\u306a\u304a\u3001\u91cd\u529b\u8a08\u7b97\u306b\u306f\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306e\u3088\u3046\u306a\u9ad8\u6b21\u7cbe\u5ea6\u306e\u6570\u5024\u7a4d\u5206\u6cd5\u3082\u3088\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u3002\u529b\u5b66\u7cfb\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u969b\u3057\u3066\u3001\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306b\u306f\u3044\u304f\u3064\u304b\u5229\u70b9\u304c\u3042\u308b\u3002\u4e00\u3064\u76ee\u306f\u3001\u6642\u9593\u53ef\u9006\u6027\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u3001n{displaystyle n} \u6bb5\u6642\u9593\u7a4d\u5206\u3057\u305f\u306e\u3061\u3001\u6642\u9593\u3092\u9006\u5411\u304d\u306b n{displaystyle n} \u6bb5\u6570\u5024\u7a4d\u5206\u3059\u308b\u3068\u3001\u521d\u671f\u4f4d\u7f6e\u306b\u623b\u308b\u3068\u3044\u3046\u6027\u8cea\u3067\u3042\u308b\u3002\u4e8c\u3064\u76ee\u306f\u3001\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u6027\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u6027\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u3002\u3053\u306e\u6027\u8cea\u306f\u3001\u8ecc\u9053\u529b\u5b66\u306b\u304a\u3044\u3066\u6709\u7528\u3067\u3042\u308b\u30024\u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306e\u3088\u3046\u306a\u4ed6\u306e\u591a\u304f\u306e\u6570\u5024\u7a4d\u5206\u6cd5\u306f\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u4fdd\u5b58\u305b\u305a\u3001\u6642\u9593\u3068\u3068\u3082\u306b\u8aa4\u5dee\u304c\u3069\u3093\u3069\u3093\u5897\u5927\u3057\u3066\u3057\u307e\u3046\u3002\u6642\u9593\u53ef\u9006\u6027\u3084\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u6027\u304b\u3089\u3001\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5\u306f\u30cf\u30df\u30eb\u30c8\u30f3\u30fb\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306b\u3082\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u3002\u30cf\u30df\u30eb\u30c8\u30f3\u30fb\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306f\u3001\u76f4\u63a5\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304c\u56f0\u96e3\u306a\u78ba\u7387\u5206\u5e03\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u30b5\u30f3\u30d7\u30eb\u3092\u5f97\u308b\u305f\u3081\u306e\u624b\u6cd5\u3067\u3042\u308b[6]\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]^ \u7267\u91ce\u6df3\u4e00\u90ce, \u798f\u91cd\u4fca\u5e78, \u5c0f\u4e45\u4fdd\u82f1\u4e00\u90ce, \u5ddd\u4e95\u6566, \u53f0\u5742\u535a, \u6749\u672c\u5927\u4e00\u90ce (2007\u5e743\u670813\u65e5). \u201cN\u4f53\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u5553\u87c4\u306e\u5b66\u6821\u6559\u79d1\u66f8\u201d.   \u56fd\u7acb\u5929\u6587\u53f0. p.\u00a048-56. 2020\u5e745\u670824\u65e5\u95b2\u89a7\u3002^ C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulations, McGraw-Hill Book Company, 1985, p. 56.^ 4.1 Two Ways to Write the Leapfrog^ Skeel, R. D., “Variable Step Size Destabilizes the St\u00f6mer\/Leapfrog\/Verlet Method”, en:BIT Numerical Mathematics, Vol. 33, 1993, p. 172\u2013175.^ Binney, James; Tremaine, Scott (2008). Galactic Dynamics (Second ed.). Princeton University Press. p.\u00a0200. ISBN\u00a0978-0-691-13027-9\u00a0^ Bishop, Christopher (2006). Pattern Recognition and Machine Learning. New York: Springer-Verlag. pp.\u00a0548\u2013554. ISBN\u00a0978-0-387-31073-2\u00a0     (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki9\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki9\/archives\/285371#breadcrumbitem","name":"\u30ea\u30fc\u30d7\u30fb\u30d5\u30ed\u30c3\u30b0\u6cd5 – Wikipedia"}}]}]