一类非线性非完整系统的Routh方程：从Chetaev条件到Euler条件

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.关键词：非线性非完整系统Routh方程Chetaev条件Vacco条件Euler条件

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

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.