Modified Lagrange method to analyze problems of sliding and rolling

A modified Lagrange method to analyze problems of sliding and rolling is pr esented. The method is based on modeling the friction as a process of colli sions between the sliding and rolling body, and particles of the surface on which it slips and rolls. The process of collisions does not need to descr ibe the exact friction process. Instead it can represent another equivalent mechanism of loss of energy of the body due to sliding and rolling. The fu nction that describes the rate of increase of the kinetic energy of the par ticles, as a result of the collisions, plays a major roll in the modified L agrange equations. Cases of isotropic and anisotropic friction can be model ed. Three examples of using the method are presented. It is shown that when art infinitely rough surface is assumed, the classical equations for nonho lonomic constraints of rolling without sliding are obtained. Lagrange multi pliers that appear in these equations obtain direct physical meaning and th e mechanism behind the constraint becomes clear. [S0021-8936(00)01404-5].