光滑曲面点接触的理想约束推导

DERIVATION OF IDEAL CONSTRAINT FOR POINT CONTACT OF TWO CURVED SURFACES WITH SMOOTH SHAPE

分析力学在讲述形状光滑的两刚性面保持点接触时,如果无摩擦或者纯滚动,使用了两个接触点的可能微小位移在接触点法向分量相等,或者接触点的相对速度为零的条件推导出接触为理想约束。本文从两曲面保持点接触时满足共点和相切的几何条件出发,获得这一结论,前提条件更加明确。

In the analytical mechanics, when two rigid surfaces with smooth shape keep contact at one point without friction or in the pure rolling state, two conditions are considered to deduce the ideal constraints for the contact. In the frictionless case, the possible infinitesimal displacements of the two contact points on the two surfaces are equal in the normal direction. In the pure rolling case, the relative velocity of the contact point is zero. In this paper, starting from the geometric conditions of taking the same position in space and in the tangent state, the preconditions are more clear and rigorous.