Projection operator techniques in Lagrangian mechanics: Symmetrically coupled oscillators.

Boyd, J.N.; Raychowdhury, P.N.

Displaying similar documents to “Projection operator techniques in Lagrangian mechanics: Symmetrically coupled oscillators.”

Breaking the symmetry of a circular system of coupled harmonic oscillators.

Boyd, J. N., Hudepohl, R. G., Raychowdhury, P. N. (2002)

International Journal of Mathematics and Mathematical Sciences

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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...

Classification of symmetries for higher order Lagrangian systems.

Manuel de León, David Martín de Diego (1994)

Extracta Mathematicae

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Classification of symmetries for higher order Lagrangian systems II: The non-autonomous case.

Manuel de León, David Martín de Diego (1994)

Extracta Mathematicae

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Representation theory of finite Abelian groups applied to a linear diatomic crystal.

Boyd, J.N., Raychowdhury, P.N. (1980)

International Journal of Mathematics and Mathematical Sciences

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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.

Mechanics

Stefan Banach

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CONTENTS Preface................ III CHAPTER I. THEORY OF VECTORS I. Operations on vectors § 1. Preliminary definitions.................. 1 § 2. Components of a vector.................. 2 § 3. Sum and difference of vectors.................. 3 § 4. Product of a vector by a number.................. 4 § 5. Components of a sum and product.................. 5 § 6. Resolution of a vector.................. 6 § 7. Scalar product.................. 7 § 8. Vector product.................. 9 § 9....

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...