Hamilton-Jacobi methods for Vakonomic Mechanics

Diogo Aguiar Gomes

doi:10.1007/s00030-007-5012-5

Hamilton-Jacobi methods for Vakonomic Mechanics

Diogo Aguiar Gomes^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	233-257
Number of pages	25
Journal	Nonlinear Differential Equations and Applications
Volume	14
Issue number	3-4
DOIs	https://doi.org/10.1007/s00030-007-5012-5
State	Published - Nov 2007
Externally published	Yes

Keywords

Hamilton-Jacobi equations
Mother theory
Vakonomic mechanics

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s00030-007-5012-5

Cite this

@article{f153f71eddf244c4b71c0f277172d842,

title = "Hamilton-Jacobi methods for Vakonomic Mechanics",

abstract = "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.",

keywords = "Hamilton-Jacobi equations, Mother theory, Vakonomic mechanics",

author = "Gomes, {Diogo Aguiar}",

year = "2007",

month = nov,

doi = "10.1007/s00030-007-5012-5",

language = "English (US)",

volume = "14",

pages = "233--257",

journal = "Nonlinear Differential Equations and Applications",

issn = "1021-9722",

publisher = "Springer Verlag",

number = "3-4",

}

TY - JOUR

T1 - Hamilton-Jacobi methods for Vakonomic Mechanics

AU - Gomes, Diogo Aguiar

PY - 2007/11

Y1 - 2007/11

N2 - 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.

AB - 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.

KW - Hamilton-Jacobi equations

KW - Mother theory

KW - Vakonomic mechanics

UR - http://www.scopus.com/inward/record.url?scp=38849191897&partnerID=8YFLogxK

U2 - 10.1007/s00030-007-5012-5

DO - 10.1007/s00030-007-5012-5

M3 - Article

AN - SCOPUS:38849191897

SN - 1021-9722

VL - 14

SP - 233

EP - 257

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 3-4

ER -

Hamilton-Jacobi methods for Vakonomic Mechanics

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this