Unified formalism for higher-order non-autonomous dynamical systems

Details Unified formalism for higher-order non-autonomous dynamical systems Unified formalism for higher-order non-autonomous dynamical systems

2011-11-25

arxiv.org/abs/1111.6020v2

J. Math. Phys. 53(3) (2012) 032901

Physics

Mathematical Physics

43 pp

Scientific paper

10.1063/1.3692326

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.

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