La théorie des perturbations au voisinage des systèmes hamiltoniens convexes
Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations
We propose a Lagrangian approach to deriving energy-preserving finite difference schemes for the Euler–Lagrange partial differential equations. Noether’s theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law. We introduce a unique viewpoint on this theorem: “the symmetry of time translation of Lagrangians derives the Euler–Lagrange equation and the energy conservation law, simultaneously.” The proposed method is a combination of a discrete counter...
Lagrangians and hamiltonians on affine bundles and higher order geometry
The higher order bundles defined by an anchored bundle are constructed as a natural extension of the higher tangent spaces of a manifold. We prove that a hyperregular lagrangian (hyperregular affine hamiltonian) is a linearizable sub-lagrangian (affine sub-hamiltonian) on a suitable Legendre triple.
Le formalisme de contact en mécanique classique et relativiste
Lepagean 2-forms in higher order Hamiltonian mechanics. I. Regularity
Lepagean 2-forms in higher order Hamiltonian mechanics. II. Inverse problem