Singularities of implicit differential systems and maximum principle

Stanisław Janeczko; Fernand Pelletier

Displaying similar documents to “Singularities of implicit differential systems and maximum principle”

Dynamical systems and Lagrangian spaces.

Obădeanu, V., Albu, I.D. (2000)

Balkan Journal of Geometry and its Applications (BJGA)

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Umbilical characteristic number of Lagrangian mappings of 3-dimensional pseudooptical manifolds

Maxim È. Kazarian (1996)

Banach Center Publications

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As shown by V. Vassilyev [V], $D_{4}^{\pm}$ singularities of arbitrary Lagrangian mappings of three-folds form no integral characteristic class. We show, nevertheless, that in the pseudooptical case the number of $D_{4}^{\pm}$ singularities counted with proper signs forms an invariant. We give a topological interpretation of this invariant, and its applications. The results of the paper may be considered as a 3-dimensional generalization of the results due to V. I. Arnold [A].

The Legendre transformation

W. M. Tulczyjew (1977)

Annales de l'I.H.P. Physique théorique

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Solving non-holonomic Lagrangian dynamics in terms of almost product structures.

Manuel de León, David Martín de Diego (1996)

Extracta Mathematicae

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Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.