Contact Dynamics versus Legendrian and Lagrangian Submanifolds
arXiv:2108.06519
Abstract
We are proposing Tulczyjew's triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit us to determine so-called generating family (obtained by merging a special contact manifold and a Morse family) for a Legendrian submanifold. Contact Hamiltonian and Lagrangian Dynamics are recast as Legendrian submanifolds of the tangent contact manifold. In this picture, the Legendre transformation is determined to be a passage between two different generators of the same Legendrian submanifold. A variant of contact Tulczyjew's triple is constructed for evolution contact dynamics.
References in corpus (8)
- Contact Hamiltonian Mechanics
- Geometry of multisymplectic Hamiltonian first-order field theories
- Contact geometry and thermodynamics of black holes in AdS spacetimes
- Remarks on Contact and Jacobi Geometry
- Tulczyjew's Triplet for Lie Groups II: Dynamics
- Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
- Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds
- Tulczyjew triples: from statics to field theory