一类非线性非完整系统的Routh方程:从Chetaev条件到Euler条件  

Routh equation of nonholonomic dynamical systems:from Chetaev condition to Euler condition

作　　者：沈惠川[1] 

机构地区：[1]中国科学技术大学天文与应用物理系统计力学中心,合肥230026

出　　处：《物理学报》2005年第6期2468-2473,共6页Acta Physica Sinica

基　　金：物理学国家理科人才培养基地基金资助的课题~~

摘　　要：对于一类其非线性约束方程可展开为关于广义速度的MacLaurin级数的非完整系统,可以在完全理想的情况下用Lagrange未定乘数法和d’Alembert原理建立其Routh方程.由此可以得到结论Chetaev条件只有在线性非完整系统中才成立并且等价于Vacco条件.引入“Euler条件”,可以统一Chetaev条件和Vacco条件,统一d’Alembert原理和Hamilton原理,并解决所有现存于非线性非完整系统中的问题.The Routh equation of a nonholonomic system with a nonlinear constraint equation that is expandable to MacLaurin progression on generalized velocity, can be obtained by Lagrangian multiplier method and d'Alembert principle in an ideal constraint condition. Chetaev condition is valid in linear nonholonomic system only, and is eguivalent to Vacco condition. The so-called 'Euler condition' can unite Chetaev condition and Vacco condition, can unite d'Alembert principle and Hamilton principle, and can resolve all existing problems in nonlinear nonholonomic system.

关 键 词：非线性非完整系统 ROUTH方程 Lagrange未定乘数法 Chetaev条件 分析力学 

分 类 号：O316[理学—一般力学与力学基础]