Unified formalism for non-autonomous mechanical systems

Abstract

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.

15 pp

References in corpus (3)

• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• Skinner-Rusk Unified Formalism for Optimal Control Systems and Applications
• Gunther's formalism (k-symplectic formalism) in classical field theory: Skinner-Rusk approach and the evolution operator

Cited by in corpus (14)

• A survey on cosymplectic geometry
• Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
• Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
• Unified formalism for higher-order non-autonomous dynamical systems
• A new multisymplectic unified formalism for second-order classical field theories
• Unified Lagrangian-Hamiltonian formalism for contact systems
• k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations
• Higher-order contact mechanics
• Noether symmetries and integrability in time-dependent Hamiltonian mechanics
• Generalized CoKähler Geometry and an Application to Generalized Kähler Structures
• Higher-order Mechanics: Variational Principles and other topics
• Unified formalism for higher-order variational problems and its applications in optimal control
• Lifted tensors and Hamilton-Jacobi separability
• Skinner-Rusk formalism for k-contact systems