×

Kane equations for general nonholonomic systems. (Chinese. English summary) Zbl 0605.70009

The representation of dynamical systems in Lagrange’s form of d’Alembert’s principle exposited by Kane and others called Kane’s equations, are extended to nonlinear nonholonomic systems of arbitrary order in this paper. It is proved without the aid of a variational principle that the extended Kane equations are the necessary and sufficient conditions for the motion of the general nonholonomic system.
It shows that the Kane equations of a general nonholonomic system can be obtained of the Kane equations of a simplified holonomic system without the nonholonomic constraints.
It is also proved that when the Mangeron equations are used in a high order nonholonomic system, it is unnecessary to equate the order of equations to the order of nonholonomic constraints. Two examples are given.
Reviewer: Liu Yanzhu

MSC:

70F25 Nonholonomic systems related to the dynamics of a system of particles
70H30 Other variational principles in mechanics
PDFBibTeX XMLCite