Integrable Hamiltonian systems on Lie groups: Kowalewski type.
Jurdjevic, V. (1999)
Annals of Mathematics. Second Series
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Jurdjevic, V. (1999)
Annals of Mathematics. Second Series
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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...
Božidar Jovanović (2012)
Publications de l'Institut Mathématique
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Ram V. Iyer, Raymond Holsapple, David Doman (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group which is also a parallelizable riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing...
V. Jurdjevic (2009)
Annales de l'I.H.P. Analyse non linéaire
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Guerra, M. (2005)
Rendiconti del Seminario Matematico
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Andrei A. Agrachev, Francesca C. Chittaro (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification...
Bernard Bonnard, Jean-Baptiste Caillau (2007)
Annales de l'I.H.P. Analyse non linéaire
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