AI 中文总结
本文推导适合本科生的经典力学中拉格朗日量的奥斯特罗格拉德斯基形式主义，提供实例、习题与应用，配套程序代码可在补充材料及GitHub获取，用于定义力学系统哈密顿形式主义。
AI 中文摘要
我们呈现了一个适合本科生水平的推导过程，涉及经典力学中依赖于构型任意阶时间导数的拉格朗日量的奥斯特罗格拉德斯基形式主义。从拉格朗日量第一变分的边界项出发，我们推导出定义力学系统哈密顿形式主义的奥斯特罗格拉德斯基公式。文中还提供了实例、习题以及相关文献应用。补充材料中讨论了一个实现该形式主义的配套计算机程序，且通过奥斯特罗格拉德斯基形式主义计算哈密顿量的代码可在补充材料及GitHub代码库中获取。
英文摘要
We present a derivation at a level suitable for undergraduates of the Ostrogradsky formalism for Lagrangians in classical mechanics that depend upon an arbitrary number of time derivatives of the configuration. From the boundary term in the first variation of the Lagrangian we derive the Ostrogradsky formulas that define the Hamiltonian formulation of mechanical systems. Worked examples, exercises, and applications to the literature are also provided. An accompanying computer program that implements the formalism is discussed in the Supplementary Materials, and code for computing Hamiltonians via the Ostrogradsky formalism is provided in the Supplementary Materials and in a GitHub repository.
CommentsAccepted for publication in the American Journal of Physics. 16 pages
