On the implicit equations of a mechanical systems motion

Abstract

It is shown that the forces acting on the points of the mechanical system may depend on their accelerations. The differential equations of a mechanical system motion prove to be implicit. It is not allowed with respect to higher derivatives. There are fundamental mathematical problems related to the possibility and the only solution of these equations with respect to higher derivatives. Implicit equations of motion are typical for mechanical systems with dry friction sliding and rolling. In the dynamics of material point such problems do not arise. But in more complex mechanical systems, including the study of the motion of a solid whole mass is concentrated at one point, as well as in systems with one degree of freedom, such a situation is very characteristic. The paper discusses four fairly simple examples of mechanical systems movement, which is described by implicit differential equations of motion.