Generalization of a new parametric formulation of mechanics for systems with variable mass

In this paper a new parametric formulation of mechanics, formulated by the author himself and based on the separation of the double role of time (independent variable and a parameter) with the aid of a family of varied paths, is extended to the arbitrary rheonomic systems with variable mass. For such systems d'Alembert–Lagrange's principle, general Hamilton's principle, and the corresponding Hamiltonian formalism are formulated, as well as the energy relations with energy change law. The obtained results are illustrated by a simple, but characteristic example.