Unified formalism for higher-order non-autonomous dynamical systems

Abstract

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.

43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition 2

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• Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
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Cited by in corpus (11)

• Geometric Hamilton-Jacobi theory for higher-order autonomous systems
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• Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians
• Higher-order Mechanics: Variational Principles and other topics
• Unified formalism for higher-order variational problems and its applications in optimal control
• Reductions of Topologically Massive Gravity II: First Order Realizations of Second Order Lagrangians
• A Lagrangian form of tangent forms
• Skinner-Rusk formalism for k-contact systems