{"topic":{"id":6207,"title":"计算运动学状态的疑问","slug":"topic","userId":1551,"categoryId":56,"createdAt":"2023-10-05 12:55:08.98844","bumpedAt":"2023-10-06 15:05:44.409373","views":518,"postsCount":3,"highestPostNumber":3,"likeCount":0,"closed":true,"pinned":false,"pinnedGlobally":false,"pinnedAt":null,"pinnedUntil":null,"isBanner":false,"excerpt":"由于运动过程中加速度始终不变（除碰撞阶段），因此速度各方向分量始终线性变化，关于速度的差分方程就绝对精确，那么四种求解运动方程还有什么区别吗","deletedAt":null,"isAnonymous":false,"isPrivate":false,"isMembersOnly":false,"category":{"id":56,"name":"计算机图形学","slug":"cg","color":"92278F"},"author":{"id":1551,"username":"pikiu","name":null,"avatarUrl":"/uploads/image/bf/ce/bfce3e19f5948ab098f937227e5ff7d6838ed44c36c164b1e317c5de87da767e.avif"},"realAuthor":{"id":1551,"username":"pikiu","name":null,"avatarUrl":"/uploads/image/bf/ce/bfce3e19f5948ab098f937227e5ff7d6838ed44c36c164b1e317c5de87da767e.avif"},"tags":[]},"posts":[{"id":12625,"postNumber":1,"raw":"由于运动过程中加速度始终不变（除碰撞阶段），因此速度各方向分量始终线性变化，关于速度的差分方程就绝对精确，那么四种求解运动方程还有什么区别吗","cooked":"

由于运动过程中加速度始终不变（除碰撞阶段），因此速度各方向分量始终线性变化，关于速度的差分方程就绝对精确，那么四种求解运动方程还有什么区别吗

\n","createdAt":"2023-10-05 12:55:09.079579","updatedAt":"2023-10-08 12:52:56.547331","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":69,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":3,"publicVersion":3,"deletedAt":null,"isAnonymous":false,"user":{"id":1551,"username":"pikiu","name":null,"avatarUrl":"/uploads/image/bf/ce/bfce3e19f5948ab098f937227e5ff7d6838ed44c36c164b1e317c5de87da767e.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":12655,"postNumber":2,"raw":"虽然匀变速运动过程中速度变化是线性的，但位移变化是非线性的。所以当时间步比较大时，用高阶方法求出的位移会比简单使用前向欧拉法更准确一点。\n\n我自己试验的时候大概跑 3 到 4 秒的仿真，如果时间步设置得大于 1/10 秒，在某些情况下就可以看出不同求解方法的区别了；如故设置得大于 1/5 秒，一般就能看出明显差异了。\n\n不过我不是做物理仿真的，可以请 @Lumi 帮忙解答一下这个问题（如果有空的话）。","cooked":"

虽然匀变速运动过程中速度变化是线性的，但位移变化是非线性的。所以当时间步比较大时，用高阶方法求出的位移会比简单使用前向欧拉法更准确一点。

我自己试验的时候大概跑 3 到 4 秒的仿真，如果时间步设置得大于 1/10 秒，在某些情况下就可以看出不同求解方法的区别了；如故设置得大于 1/5 秒，一般就能看出明显差异了。

不过我不是做物理仿真的，可以请 @Lumi 帮忙解答一下这个问题（如果有空的话）。

\n","createdAt":"2023-10-05 14:22:04.006748","updatedAt":"2023-10-05 14:34:34.842114","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":178,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":1381,"username":"greyishsong","name":"greyishsong","avatarUrl":"/uploads/image/da/bc/dabc731b0311f59850625bbeb55ed969fcfac0430c5ef0f68441e5466b7aa496.avif","admin":false,"moderator":true,"signatureRaw":null,"signatureCooked":null}},{"id":12786,"postNumber":3,"raw":"其实我的意思是，似乎**隐式欧拉法**和**半隐式欧拉法**的函数实现完全相同，是我理解上出问题了吗 \n :upside_down_face:\n\n# 这是隐式欧拉法\n

\n\n![image|690x101](/uploads/image/65/21/652151ecaaee9f0205b69c8ebebd01b005eef921e783527bd226c33405817d94.avif)\n\n\n

\n
\n\n# 这是半隐式欧拉法\n

\n\n![image|690x109](/uploads/image/03/ca/03ca5338263cf48e6348f3a9c09ca0e37649f9080b80e824287c8dedbf24c268.avif)\n\n\n

\n\n## 半隐式法举的例子\n

\n\n![image|690x385](/uploads/image/b5/3e/b53e2802fa45ac22bbdefd78add43fb1d712bd5e1f34d8fe2e3ce753e1d6a612.avif)\n\n\n

","cooked":"

其实我的意思是，似乎隐式欧拉法和半隐式欧拉法的函数实现完全相同，是我理解上出问题了吗
\n🙃

这是隐式欧拉法

$\"image\"$

\n
\n

这是半隐式欧拉法

$\"image\"$

半隐式法举的例子

$\"image\"$

","createdAt":"2023-10-06 15:05:44.409373","updatedAt":"2023-10-06 15:05:44.409373","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":86,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":1551,"username":"pikiu","name":null,"avatarUrl":"/uploads/image/bf/ce/bfce3e19f5948ab098f937227e5ff7d6838ed44c36c164b1e317c5de87da767e.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}}],"hasMore":false,"lastReadPostNumber":3,"hasUrlPostNumber":true}