Displaying similar documents to “First integrals for two linearly coupled nonlinear Duffing oscillators.”

Symmetries and currents in nonholonomic mechanics

Michal Čech, Jana Musilová (2014)

Communications in Mathematics

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In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical...

Conservation laws and symmetry in economic growth models: a geometrical approach.

Manuel de León, David Martín de Diego (1998)

Extracta Mathematicae

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The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian...

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...