Lie algebroids in classical mechanics and optimal control

DOI10.3842/SIGMA.2007.050zbMath1142.49023arXivmath-ph/0703062MaRDI QIDQ2473447

Yanyan Li

Publication date: 27 February 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0703062

zbMATH Keywords

variational calculusLie algebroidsLagrangian mechanicsoptimal control systemsreduction of dynamical systems

Mathematics Subject Classification ID

Geometric methods (93B27) Hamilton's principle (70H25) Variational principles of physics (49S05)

Related Items (17)

Second-order constrained variational problems on Lie algebroids: applications to optimal control ⋮ On almost complex Lie algebroids ⋮ Second-order variational problems on Lie groupoids and optimal control applications ⋮ Discrete variational optimal control ⋮ Unnamed Item ⋮ Higher-order variational calculus on Lie algebroids ⋮ Euler-Lagrange-Herglotz equations on Lie algebroids ⋮ Remarks on generalized Lie algebroids and related concepts ⋮ Classical field theory on Lie algebroids: multisymplectic formalism ⋮ Lagrangian mechanics and reduction on fibered manifolds ⋮ An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems ⋮ Lie algebroids generated by cohomology operators ⋮ Models for higher algebroids ⋮ Complex Lie algebroids and Finsler manifold in time-dependent fractal dimension and their associated decomplexifications ⋮ Morse families and Dirac systems ⋮ Global controllability tests for geometric hybrid control systems ⋮ Low order-value optimization and applications

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