Symmetry Methods in Lagrangian and Hamiltonian Systems

Abstract

The aim of this research is to discuss and study symmetries of Lagrangian and Hamiltonian systems using Lie algebra of the symmetry Lie groups. In particular conservation laws for invariant variational based on Noether theorem. We introduced analytical and geometrical formulation of Lagrangian and Hamiltonian systems that contain symmetry rules on the vector space by using classical variational calculus. Also we obtained the reduction of controlled Lagrangian and Hamiltonian systems with symmetry. Finally we classify the symmetry groups of Hamiltonian system with degrees of freedom and we provided some application of symmetries of Lagrangian and Hamiltonian systems.