Integrating factors and conservation theorems for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems

We present a general approach to the construction of conservation laws for variable mass nonholonomic nonconservative systems. First, we give the definition of integrating factors, and we study in detail the necessary conditions for the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally, we give an example to illustrate the application of the results.