Unified formalism for non-autonomous mechanical systems

Details Unified formalism for non-autonomous mechanical systems Unified formalism for non-autonomous mechanical systems

2008-03-28

arxiv.org/abs/0803.4085v1

Physics

Mathematical Physics

15 pp

Scientific paper

10.1063/1.2929668

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (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, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

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