Hamilton-Jacobi methods for vakonomic mechanics. (English) Zbl 1135.37327

Gomes, Diogo Aguiar

NoDEA, Nonlinear Differ. Equ. Appl. 14, No. 3-4, 233-257 (2007).

Summary: We extend the theory of Aubry-Mather measures to Hamiltonian systems that arise in vakonomic mechanics and sub-Riemannian geometry. We use these measures to study the asymptotic behavior of (vakonomic) action-minimizing curves, and prove a bootstrapping result to study the partial regularity of solutions of convex, but not strictly convex, Hamilton-Jacobi equations.

MSC:

37J50	Action-minimizing orbits and measures (MSC2010)
37J60	Nonholonomic dynamical systems
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
70H20	Hamilton-Jacobi equations in mechanics

Keywords:

Mother theory; Hamilton-Jacobi equations; viscosity solutions; regularity; duality; Hamiltonian systems; sub-Riemannian geometry; action-minimizing curves