Tulczyjew triples: from statics to field theory

Abstract

We propose a geometric approach to dynamical equations of physics, based on the idea of the Tulczyjew triple. We show the evolution of these concepts, starting with the roots lying in the variational calculus for statics, through Lagrangian and Hamiltonian mechanics, and concluding with Tulczyjew triples for classical field theories, illustrated with a numer of important examples.

corrected version, presentation improved (26 pages, 14 figures)

References in corpus (6)

• Tangent Lifts of Poisson and Related Structures
• Dirac Algebroids in Lagrangian and Hamiltonian Mechanics
• Graded bundles and homogeneity structures
• Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
• The Tulczyjew triple for classical fields
• Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds

Cited by in corpus (4)

• A novel approach to contact Hamiltonians and contact Hamilton-Jacobi theory
• A Hamilton-Jacobi formalism for higher order implicit systems
• Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings
• Contact Dynamics versus Legendrian and Lagrangian Submanifolds