Noether Theorems for Dynamical Systems with Non-standard Lagrangians based on El-Nabulsi Models

Abstract:

The Noether theorems for dynamical systems with non-standard Lagrangians based on El-Nabulsi models are studied. The Hamilton principles with exponential Lagrangians and power law Lagrangians are established respectively, and the Euler-Lagrange equations of the systems are obtained. The formulation of the conditions of Noether (quasi-) symmetrical transformations are given in terms of invariance of Hamilton action under infinitesimal transformation, the Noether theorems of dynamical systems with non-standard Lagrangians are established. At the end of the article, two examples are given to illustrate the application of the results.