摘要
研究了本质线性非完整系统的Hamilton原理,分别应用与不应用Appell—Chetaev条件证明了本质线性非完整系统Hamilton变分泛函取驻值的充分必要条件.结果表明,在本质线性非完整系统中,Hamilton 作用量是稳定的作用量,与完整系统的Hamilton原理具有相同的形式与本质;而且由Hamilton原理得到的运动方程不会导致任何力学与数学上的矛盾.最后给出了Hamilton原理向本质非线性非完整系统推广时产生数学与力学上不合理的根本原因.
The Hamilton principle of intrinsical linear nonholonomic system was studied. The sufficient and necessary conditions of stationary for Hamilton variational function are given and proved by using Appell-Chetaev condition or not. The results show that the Hamilton's action variable is a stable one in instrinsical linear nonholonomic system and the Hamilton principle is similar to that of holonomic system. There are no mechanical or mathematical contradications in the equations of motion gotten from the Hamilton principle. Finally, the essential reasons are given why it is unconscionable for the Hamilton principle to be generalized to the intrinsical nonlinear nonholonomic system.
出处
《动力学与控制学报》
2004年第1期32-36,共5页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(10272041).~~
