Timelike trajectories with fixed energy under a potential in static spacetimes.
Germinario, Anna (2006)
International Journal of Mathematics and Mathematical Sciences
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Germinario, Anna (2006)
International Journal of Mathematics and Mathematical Sciences
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Fabio Giannoni, Antonio Masiello (1995)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this Note, by using a generalization of the classical Fermat principle, we prove the existence and multiplicity of lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds, satisfying a suitable compactness assumption, which is weaker than the globally hyperbolicity.
Shun-Cheng Chang (1993)
Mathematische Zeitschrift
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F. Giannoni, A. Masiello, P. Piccione (1998)
Annales de l'I.H.P. Physique théorique
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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...
Ugo Boscain, Francesco Rossi (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Fix two points and two directions (without orientation) of the velocities in these points. In this paper we are interested to the problem of minimizing the cost
along all smooth curves starting from
Bartolo, Rossella (2003)
International Journal of Mathematics and Mathematical Sciences
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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...
Udrişte, Constantin (1996)
Balkan Journal of Geometry and its Applications (BJGA)
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