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On the validity of the Euler–Lagrange equation
, 2005
"... The purpose of the present paper is to establish the validity of the Euler–Lagrange equation for the solution ˆx to the classical problem of the calculus of variations. ..."
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The purpose of the present paper is to establish the validity of the Euler–Lagrange equation for the solution ˆx to the classical problem of the calculus of variations.
PERIODIC SOLUTIONS OF LAGRANGE EQUATIONS
, 2003
"... Nontrivial periodic solutions of Lagrange Equations are investigated. Sublinear and superlinear nonlinearity are included. Convexity assumptions are significiently relaxed. The method used is the duality developed by the authors. ..."
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Nontrivial periodic solutions of Lagrange Equations are investigated. Sublinear and superlinear nonlinearity are included. Convexity assumptions are significiently relaxed. The method used is the duality developed by the authors.
The reduced EulerLagrange equations
 Fields Institute Comm
, 1993
"... Marsden and Scheurle [1993] studied Lagrangian reduction in the context of momentum map constraints—here meaning the reduction of the standard EulerLagrange system restricted to a level set of a momentum map. This provides a Lagrangian parallel to the reduction of symplectic manifolds. The present ..."
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Cited by 45 (16 self)
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. For unconstrained systems, we use a velocity shifted Lagrangian, which plays the role of the Routhian in the constrained theory. Hamilton’s variational principle for the EulerLagrange equations breaks up into two sets of equations that represent a set of EulerLagrange equations with gyroscopic forcing that can
On the global version of EulerLagrange equations
 J. Phys. A
"... Abstract. The introduction of a covariant derivative on the velocity phase space is needed for a global expression of EulerLagrange equations. The aim of this paper is to show how its torsion tensor turns out to be involved in such a version. ..."
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Cited by 4 (0 self)
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Abstract. The introduction of a covariant derivative on the velocity phase space is needed for a global expression of EulerLagrange equations. The aim of this paper is to show how its torsion tensor turns out to be involved in such a version.
Invariant EulerLagrange equations and the invariant variational bicomplex
, 2003
"... In this paper, we derive an explicit groupinvariant formula for the EulerLagrange equations associated with an invariant variational problem. The method relies on a groupinvariant version of the variational bicomplex induced by a general equivariant moving frame construction, and is of independe ..."
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Cited by 41 (29 self)
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In this paper, we derive an explicit groupinvariant formula for the EulerLagrange equations associated with an invariant variational problem. The method relies on a groupinvariant version of the variational bicomplex induced by a general equivariant moving frame construction
Linearization Methods For Variational Integrators And EulerLagrange Equations
"... Hamiltonian systems arise in a wide variety of idealized physical systems and Hamilton's equations often must be solved numerically. In general, traditional finite difference methods for numerically integrating ordinary differential equations do not take into account the special structure of Ha ..."
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of Hamilton's equations. One would like the numerical solution to preserve some or all of the properties of the continuous time solution. Variational integrators, also called discrete EulerLagrange equations in this thesis, provide a way to do that. This thesis is about differentiating, i.e linearizing
On the bounded slope condition and the validity of the Euler–Lagrange equation
 SIAM J. Control Optim
"... Abstract. Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. An application of this result to prove the validity of the Euler Lagrange equation for w is presented. ..."
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Cited by 12 (0 self)
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Abstract. Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. An application of this result to prove the validity of the Euler Lagrange equation for w is presented.
Fractional Euler–Lagrange Equations of Motion in Fractional Space
, 2006
"... Abstract: Fractional variational principles have gained considerable importance during the last decade due to their various applications in several areas of science and engineering. In this study, the fractional Euler– Lagrange equations corresponding to a prescribed fractional space are obtained. T ..."
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Cited by 3 (0 self)
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Abstract: Fractional variational principles have gained considerable importance during the last decade due to their various applications in several areas of science and engineering. In this study, the fractional Euler– Lagrange equations corresponding to a prescribed fractional space are obtained
VARIATIONAL C ∞ −SYMMETRIES AND EULERLAGRANGE EQUATIONS
"... A generalization of the concept of variational symmetry, based on λ−prolongations, allows us to construct new methods of reduction for EulerLagrange equations. An adapted formulation of the Noether’s theorem for the new class of symmetries is presented. Some examples illustrate how the method works ..."
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Cited by 7 (0 self)
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A generalization of the concept of variational symmetry, based on λ−prolongations, allows us to construct new methods of reduction for EulerLagrange equations. An adapted formulation of the Noether’s theorem for the new class of symmetries is presented. Some examples illustrate how the method
AVdifferential geometry: EulerLagrange equations
, 2006
"... A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and unifies various geometrical approaches to mechanics in the L ..."
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Cited by 13 (9 self)
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in the Lagrangian and Hamiltonian pictures, including timedependent lagrangians and hamiltonians. In our approach, lagrangians and hamiltonians are, in general, sections of certain Rprincipal bundles, and the solutions of analogs of EulerLagrange equations are curves in certain affine bundles. The correct
Results 1  10
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