Unified Lagrangian-Hamiltonian formalism for contact systems

Abstract

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of contact autonomous mechanical systems, which is based on the approach of the pionnering work of R. Skinner and R. Rusk. This framework permits to skip the second order differential equation problem, which is obtained as a part of the constraint algorithm (for singular or regular Lagrangians), and is specially useful to describe singular Lagrangian systems. Some examples are also discussed to illustrate the method.