Herglotz type conservation laws for nonconservative nonholonomic systems

The Herglotz variational principle offers an effective method for studying nonconservative system dynamics. The aim of this paper is to study the conservation laws of nonholonomic systems by using the Herglotz type generalized variational principle and establish Noether's theorem and its inverse theorem for this system. In deriving the equations of motion, we use the Suslov definition of the reciprocity relation between differential and variational operations. First, the Herglotz type generalized variational principle is listed, and the Herglotz type Chaplygin equations for nonconservative nonholonomic systems are deduced. Second, Noether's theorem and Noether's inverse theorem are established, and the Herglotz type conservation laws are given. Finally, an example is provided to illustrate the practical implementation of the findings.