摘要
本文提出并证明了分析动力学中的各级不完全的广义变分原理和一个完全的广义变分原理.文中首次把开关函数应用于变分原理,使论述简洁明了.在这些变分原理中,动力学方程、初始位置条件、终了位置条件和几何约束条件,全部或者部分地不是事先必须满足的,即它们已成为变分原理的自然条件,因此给试函数的设计和分析力学的变分计算提供了一种新的有效的方法.
The completely generalized variational principle in analytical dynamics is presented in this paper. Applying the completely generalized variational principle, when the test functions are being construced, both the dynamic equations, and the initial position end position conditions and the geometric constraint conditions are not necessary to be satisfied beforehand, since all of them have been turned to become the natural conditions of the variational principle. According to the completely generalized variational principle, the classical Hamilton's principleand the generalized variational prirciples at any levels are able to be derived.
关键词
分析动力学
广义变分原理
开关参数
Analytic dynamics
Generalized variational principles
Switching parameter
