关键词: nonholonomic system, Lagrange’s theorem, manifold, stability, Liapunov’s direct method

Abstract: The stability problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied 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.

Key words: nonholonomic system, Lagrange’s theorem, manifold, stability, Liapunov’s direct method