Displaying similar documents to “Characterization of higher-order tangent bundles.”

Non-holonomic mechanical systems in jet bundles.

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.

On complete solutions and complete singular solutions of second order ordinary differential equations

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...

A geometric analysis of dynamical systems with singular Lagrangians

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.

A new geometric setting for classical field theories

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.

Symmetries of a dynamical system represented by singular Lagrangians

Monika Havelková (2012)

Communications in Mathematics

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Dynamical properties of singular Lagrangian systems differ from those of classical Lagrangians of the form L = T - V . Even less is known about symmetries and conservation laws of such Lagrangians and of their corresponding actions. In this article we study symmetries and conservation laws of a concrete singular Lagrangian system interesting in physics. We solve the problem of determining all point symmetries of the Lagrangian and of its Euler-Lagrange form, i.e. of the action. It is known that...