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 引用本文: 肖静, 刘畅, 王勇. 基于Frobenius定理的Hamilton-Jacobi方法的几何解释[J]. 应用数学和力学, 2017, 38(6): 708-714.
XIAO Jing, LIU Chang, WANG Yong. A Geometric Explanation of Hamilton-Jacobi Methods Based on the Frobenius Theorem[J]. Applied Mathematics and Mechanics, 2017, 38(6): 708-714. doi: 10.21656/1000-0887.370268
 Citation: XIAO Jing, LIU Chang, WANG Yong. A Geometric Explanation of Hamilton-Jacobi Methods Based on the Frobenius Theorem[J]. Applied Mathematics and Mechanics, 2017, 38(6): 708-714.

• 中图分类号: O316

## A Geometric Explanation of Hamilton-Jacobi Methods Based on the Frobenius Theorem

Funds: The National Natural Science Foundation of China（11572145;11202090）;China Postdoctoral Science Foundation（2014M560203）
• 摘要: 给出了一阶偏微分方程特征微分方程组的一种基于Frobenius定理的几何解释，通过研究发现根据Frobenius定理可以从一阶偏微分方程直接得到其特征微分方程组；在此基础上说明如何利用几何方法从Hamilton正则方程出发找到与之对应的Hamilton-Jacobi方程.这种方法可以被用于非保守或非完整Hamilton力学问题的研究中，经典Hamilton-Jacobi方法是这种方法的一个特例.
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##### 出版历程
• 收稿日期:  2016-09-05
• 修回日期:  2016-09-30
• 刊出日期:  2017-06-15

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