Helmholtz theorem for Hamiltonian systems on time scales

Abstract

We derive the Helmholtz theorem for Hamiltonian systems defined on time scales in the context of nonshifted calculus of variations which encompass the discrete and continuous case. Precisely, we give a theorem characterizing first order equation on time scales, admitting a Hamiltonian formulation which is defined with non-shifted calculus of variation. Moreover, in the affirmative case, we give the associated Hamiltonian.

References in corpus (3)

• Calculus of Variations on Time Scales with Nabla Derivatives
• Differential, integral, and variational delta-embeddings of Lagrangian systems
• Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

Cited by in corpus (2)

• Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
• Helmholtz theorem for stochastic Hamiltonian systems