相空间中非完整非保守力学系统的一个动力学逆问题  

An Inverse Problem of a Nonholonomic Non-conservative Mechanical System in Phase Space

作　　者：张毅[1] 

机构地区：[1]苏州科技学院土木工程学院,江苏苏州215011

出　　处：《兵工学报》2012年第5期600-604,共5页Acta Armamentarii

基　　金：国家自然科学基金项目(10972151)

摘　　要：研究了相空间中非完整非保守系统的动力学逆问题。分别建立了相空间中完整非保守系统和非完整非保守系统的运动微分方程,将系统的一个已知积分对时间求导数,引入Еругин函数,得到一个一阶常微分方程,分别考虑非保守力仅依赖于广义坐标和仅依赖于广义动量两种情况,由这个一阶常微分方程并利用系统的运动微分方程得到了确定非保守力的代数方程组,系统的非保守力可通过解此代数方程组来确定。文中举例说明了结果的应用。A dynamical inverse problem of a nonholonomic non-conservative system in phase space was studied.The differential equations of motion were established for non-conservative and nonholonomic non-conservative systems in phase space,respectively.A first-order ordinary differential equation was obtained by differentiating a known integral of the system with respect to time and introducing the Erugin function.Under two circumstances of which the non-conservative forces only rely on generalized coordinates and only rely on generalized momentum,the algebraic equations for determining the non-conservative forces were obtained by the first-order ordinary differential equation and using the differential equations of motion of the systems.The non-conservative forces of the systems can be determined by solving the above algebraic equations.Some examples were given to illustrate the application of the results.

关 键 词：基础力学 动力学逆问题 非保守系统 非完整系统 Bertrand定理 

分 类 号：O316[理学—一般力学与力学基础]