Lie algebroids in classical mechanics and optimal control.
Martínez, Eduardo (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Displaying similar documents to “Variational calculus on Lie algebroids”
Lie algebroids in classical mechanics and optimal control.
Lie algebroids and mechanics
Paulette Libermann (1996)
Archivum Mathematicum
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We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold ; the set of units is the zero section identified with the manifold . We study the Legendre transformation on Lie algebroids.
On Lie algebroid actions and morphisms
Tahar Mokri (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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A criterion for the minimal closedness of the Lie subalgebra corresponding to a connected nonclosed Lie subgroup.
Jan Kubarski (1991)
Revista Matemática de la Universidad Complutense de Madrid
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Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric
Claudio Altafini (2004)
ESAIM: Control, Optimisation and Calculus of Variations
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For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian...