Hamilton’s Principle and Noether’s Theorem

Abstract This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses Noether’s theorem, a method for using symmetries of the extended Lagrangian to identify quantities that are conserved during the motion of the system. Noether’s theorem is a powerful technique for discovering conserved quantities in complex Lagrangian systems. The basics of the method are analysed in the simple context of Lagrangian systems with a finite number of degrees of freedom.