Classical Lagrangian and Hamiltonian Dynamics

Abstract

The classical development is followed in the case where the configuration manifold is the vector space \(\mathbb{R}^{n}\). A Lagrangian function \(L: \mathbb{R}^{n} \rightarrow \mathbb{R}^{1}\) is introduced and variational methods are used to derive Euler–Lagrange equations and Hamilton’s equations. Several mechanical systems are studied to illustrate the developments.