Classification of noether symmetries for Lagrangians with three degrees of freedom

Abstract

The noether symmetries of the Euler-Lagrange equations for a Hamiltonian system with three degrees were classified. All groups were classified that appeared as symmetries of a general Hamiltonians system of n degrees of freedom. It is noted that Noether's theorem associates a conservation for the Euler-Lagrange equations with each variational symmetry. It was observed that translation invariance leads to the conservation of angular momentum, and time translation invariance leads to conservation of energy.