Publication

Multisymplectic Lie group variational integrator for a geometrically exact beam in R3

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures
2014
Journal Articles

Abstract

In this paper we develop, study, and test a Lie group multisymplectic integra- tor for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions.

Official source

https://infoscience.epfl.ch/entities/publication/06734b8c-b062-42bd-951a-bd9abaff8efa

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Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures
2014
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/06734b8c-b062-42bd-951a-bd9abaff8efa

About this result

Related concepts (9)

Covariant formulation of classical electromagnetism

The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These expressions both make it simple to prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, and also provide a way to translate the fields and forces from one frame to another.

Lagrangian mechanics

In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, Mécanique analytique. Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space and a smooth function within that space called a Lagrangian. For many systems, where and are the kinetic and potential energy of the system, respectively.

Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.

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