Method of variation of parameters for solving a constrained Birkhoffian system  

求解约束Birkhoff系统的参数变异法(英文)

作　　者：张毅[1] 

机构地区：[1]苏州科技学院土木工程学院,苏州215011

出　　处：《Journal of Southeast University(English Edition)》2013年第3期342-345,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.10972151,11272227)

摘　　要：For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.为了深入研究约束力学系统的积分问题,讨论了具有约束的Birkhoff系统的积分方法问题,提出用参数变异法求解约束Birkhoff系统的动力学方程.首先,建立约束Birkhoff系统及相应的自由Birkhoff系统的运动微分方程;其次,构建辅助方程系统,并找到其一般解;最后,变异参数并利用Birkhoff系统的广义正则变换的性质,获得问题的解.该方法揭示了自由Birkhoff系统和约束Birkhoff系统的解之间的内在联系.所提研究方法和结果具有普遍意义,可进一步应用于各种约束力学系统,例如,非保守系统和非完整约束系统等.

关 键 词：Birkhoffian mechanics method of integration method of variation of parameter constrained Birkhoffian system 

分 类 号：O316[理学—一般力学与力学基础]