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

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 ± 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 ± 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].

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.