منابع مشابه
Multi-Time Euler-Lagrange Dynamics∗
This paper introduces new types of Euler-Lagrange PDEs required by optimal control problems with performance criteria involving curvilinear or multiple integrals subject to evolutions of multidimensional-flow type. Particularly, the anti-trace multi-time Euler-Lagrange PDEs are strongly connected to the multi-time maximum principle. Section 1 comments the limitations of classical multi-variable...
متن کاملEuler-lagrange Equations
. Consider a mechanical system consisting of N particles in R subject to some forces. Let xi ∈ R denote the position vector of the ith particle. Then all possible positions of the system are described by N -tuples (x1, . . . , xN ) ∈ (R) . The space (R) is an example of a configuration space. The time evolution of the system is described by a curve (x1(t), . . . , xN (t)) in (R) and is governed...
متن کاملThe Reduced Euler-Lagrange Equations
Marsden and Scheurle [1993] studied Lagrangian reduction in the context of momentum map constraints—here meaning the reduction of the standard Euler-Lagrange system restricted to a level set of a momentum map. This provides a Lagrangian parallel to the reduction of symplectic manifolds. The present paper studies the Lagrangian parallel of Poisson reduction for Hamiltonian systems. For the reduc...
متن کاملEuler-Lagrange equations and geometric mechanics on Lie groups with potential
Abstract. Let G be a Banach Lie group modeled on the Banach space, possibly infinite dimensional, E. In this paper first we introduce Euler-Lagrange equations on the Lie group G with potential and right invariant metric. Euler-Lagrange equations are natural extensions of the geodesic equations on manifolds and Lie groups. In the second part, we study the geometry of the mechanical system of a r...
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Nonlocally related systems for the Euler and Lagrange systems of twodimensional dynamical nonlinear elasticity are constructed. Using the continuity equation, i.e., conservation of mass of the Euler system to represent the density and Eulerian velocity components as the curl of a potential vector, one obtains the Euler potential system that is nonlocally related to the Euler system. It is shown...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Physics
سال: 2014
ISSN: 2327-4352,2327-4379
DOI: 10.4236/jamp.2014.213138