关键词: 点接触, 约束方程, 非完整约束, Appell-Chetaev 条件

Abstract:

Nonholomonic constraints are involved for 3D point-contact problems. The virtual displacements restricted by the constraints are usually given by Appell-Chetaev’s rule. It has not been very clear of the geometric meaning in configuration space for Appell-Chetaev’s rule of nonholonomic constraints. The authors investigate point contact with pure rolling by two rigid bodies in a multibody system to discover its geometric sense. First, the sufficient and necessary conditions of point contact are given. A ball-plane system is presented to demonstrate the validation of the conditions by deducing the system’s obvious contact constraint originating from them. Two geometric restrictions for pure rolling are obtained by the nonholonomic constraints of pure rolling as well as the contact constraint in velocity level. It proves that the virtual displacements of the two restrictions are same as those of the constraints of point contact with pure rolling obtained by Appell-Chetaev’s rule. So, it is thought that the constraints of pure rolling are constructed by the two geometric restrictions.

Key words: point contact, constraint equation, nonholonomic constraint, Appell-Chetaev’s rule