Unified formalism for nonautonomous mechanical systems.

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and nonregular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk [“Generalized Hamiltonian dynamics I. Formulation on T*QxTQ,” J. Math. Phys. 24, 2589 (1983)]. The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, a semidiscretization of the nonlinear wave equation is studied, proving the applicability of the proposed formalism. [ABSTRACT FROM AUTHOR]