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Manuel de León, David Martín de Diego (1996)
Extracta Mathematicae
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In this paper we present a geometrical formulation for Lagrangian systems subjected to non-holonomic constraints in terms of jet bundles. Cosymplectic geometry and almost product structures are used to obtained the constrained dynamics without using Lagrange multipliers method.
M. De León, E. Merino, J. A. Oubiña, M. Salgado (1994)
Annales de l'I.H.P. Physique théorique
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Manuel De León, Eugenic Merino, José A. Oubiña, Modesto Salgado (1995)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Zhou, W.S., Cai, S.F. (2006)
Lobachevskii Journal of Mathematics
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Masatomo Takahashi (2007)
Colloquium Mathematicae
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A complete solution of an implicit second order ordinary differential equation is defined by an immersive two-parameter family of geometric solutions on the equation hypersurface. We show that a completely integrable equation is either of Clairaut type or of first order type. Moreover, we define a complete singular solution, an immersive one-parameter family of singular solutions on the contact singular set. We give conditions for existence of a complete solution and a complete singular...
Monika Havelková (2011)
Communications in Mathematics
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We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.
M. de León, J. C. Marrero, D. Martín de Diego (2003)
Banach Center Publications
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A new geometrical setting for classical field theories is introduced. This description is strongly inspired by the one due to Skinner and Rusk for singular lagrangian systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.