Abstract:

In this article, we discuss the G-Hamiltonian system which is a generalization of the traditional Hamiltonian system in mechanics. Moreover, we demonstrate that when given a G-Hamiltonian system of differential equations, such as dx/dt=Ax, the transformations that have this form dy/dt=BA^{-1}By are also G-Hamiltonian. Furthermore, we discuss the G-Lagrangian structure which is a generalization of the traditional Lagrangian formulation in mechanics.