×

zbMATH — the first resource for mathematics

Hamilton-Jacobi methods for vakonomic mechanics. (English) Zbl 1135.37327
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
PDF BibTeX XML Cite
Full Text: DOI