Herglotz-d’Alembert principle and conservation laws for nonholonomic systems with variable mass

Variable mass systems are ubiquitous in nature and engineering. The aim of this paper is to extend the Herglotz generalized variational principle to variable mass nonholonomic systems. In this paper, Herglotz conservation laws of variable mass nonholonomic systems are studied. The Herglotz generalized variational principle of variable mass nonholonomic systems is established, and the Herglotz-d’Alembert principle for nonholonomic systems with variable mass is derived, in which the Hölder definition of commutative relation is used. The transformation of the invariance condition of Herglotz-d’Alembert principle is established by introducing the generators of space and time. Herglotz conservation theorem and its inverse for variable mass nonholonomic systems are constructed based on this principle. In the end, an example is used as a proof of this application.