三类非完整变分下的约束运动微分方程  

Differential equations of motion for constrained systems with respect to three kinds of nonholonomic variations

作　　者：赵喆[1] 郭永新[2] 刘畅[3] 刘世兴[2] 

机构地区：[1]沈阳药科大学基础学院,沈阳110016 [2]辽宁大学物理学院,沈阳110036 [3]北京理工大学理学院,北京100081

出　　处：《物理学报》2008年第4期1998-2005,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10472040);辽宁省优秀青年科研人才培养基金(批准号:3040005);教育部留学回国人员科研启动基金(批准号:2004527);教育部春晖计划(批准号:Z2005-1-21006);辽宁省教育厅基础研究计划(批准号:05L155)资助的课题~~

摘　　要：在分析三类不等价的非完整变分,即vakonomic变分、Suslov变分和Hlder变分的基础上,利用Lagrange乘子法和稳定作用量原理,讨论非线性非完整约束系统在这三类变分下的运动微分方程,论证了这三类微分方程等价的条件.作为一般约束系统的特例,得到了仿射非完整约束系统的运动微分方程.最后借助两个实例验证了结论的正确性.Based on an analysis of three kinds of non-equivalent nonholonomic variations, i.e., the Suslov＇s variation, Holder＇s variation and vakonomic variation, the method of Lagrange multipliers and stationary action principle are utilized to discuss the differential equations of motion for nonlinear nonholonomic constrained systems with respect to the three kinds of variations. The condition for the three kinds of equations to be equivalent is investigated. The equations for affine nonholonomic constrained systems are also obtained as special cases of the general nonholonomic systems. Two examples are given to illustrated the validity of the result.

关 键 词：非完整约束 Chetaev条件 vakonomie动力学 LAGRANGE乘子法 

分 类 号：O316[理学—一般力学与力学基础]