一类非完整系统的Lagrange定理及其应用

Lagrange′s Theorem for a Class of Nonholonomic Systems and Its Application

本文研究一类非完整系统平衡位置流形的稳定性问题·利用Ляпунов直接法和稳定性定义将完整系统的Ｌａｇｒａｎｇｅ定理推广到一类非完整保守系统与耗散系统，并对该类非完整系统平衡位置流形的渐近稳定性与耗散力间的关系作了新的表述，最后举例说明定理的应用·

The stability problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied in this paper.Based on Liapunov′s direct method and the definition of stability,Lagrange′s theorem of holonomic systems is extended to a class of nonholonomic conservative systems and dissipative systems,and a new expression is made to the relation between asymptotic stability for the manifold of equilibrium positions of this class of nonholonomic systems and dissipative forces.Two examples are finally given to illustrate the application of the theorems.