Implicit contact dynamics and Hamilton-Jacobi theory - Esen, Ogul; Valcazar, Manuel Lainz; de Leon, Manuel; Sardon, Cristina (Elsevier, 2023)
In this paper, we introduce implicit Hamiltonian dynamics in the framework of contact geometry in two different ways: first, we introduce classical implicit Hamiltonian dynamics on a contact manifold, followed by evolution Hamiltonian dynamics. In the first case, implicit contact Hamiltonian dynamics is defined as a Legendrian submanifold of a tangent contact space, whilst the implicit evolution dynamic is understood as a Lagrangian submanifold of a certain symplectic space embedded into the tangent contact space. To conclude, we propose a geometric Hamilton-Jacobi theory for both of these formulations.& COPY; 2023 Elsevier B.V. All rights reserved.
Keywords: Contact manifolds; Implicit dynamics; Hamilton-Jacobi theorem