From Euler-Lagrange equations to canonical nonlinear connections

Mircea Neagu

Displaying similar documents to “From Euler-Lagrange equations to canonical nonlinear connections”

The geometry of autonomous metrical multi-time Lagrange space of electrodynamics.

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A direct geometrical construction of the dynamics of non-holonomic Lagrangian systems.

W. Sarlet (1996)

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Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Ján Brajerčík (2011)

Czechoslovak Mathematical Journal

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Let $μ : F X \to X$ be a principal bundle of frames with the structure group ${Gl}_{n} (ℝ)$ . It is shown that the variational problem, defined by ${Gl}_{n} (ℝ)$ -invariant Lagrangian on $J^{r} F X$ , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.

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.