We study a set of cohomology classes which emerge in the cohomological formulations calculus variations as obstructions to existence (global) solutions Euler–Lagrange equations Chern–Simons gauge theories higher dimensions [Formula: see text].

When space-time is assumed to be non-Riemannian the minimal coupling procedure (MCP) is not compatible, in general, with minimal action principle (MAP). This means that the equations gotten by applying MCP to the Euler-Lagrange equations of a Lagrangian L do not coincide with the Euler-Lagrange equations of the Lagrangian obtained by applying MCP to L. Such compatibility can be restored if the ...

Euler–Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global equations of motion. Both continuous equations of motion and variational integrators completely avoid the singularities and complexities introduced by local...

Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler-Lagrange equations, culminating in a blow up analysis.

In the context of offshore oil production, we are interested in accurate and fast computation of two-phase flows in pipelines. A one dimensional model of hyperbolic equations is solved numerically by an explicit Lagrange Euler projection method. This paper shows that adaptive multiresolution techniques can speed up the computation significantly. Even more so when local time stepping enhancement...

We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and verifying that it leads to the correct solution to the Euler-Lagrange equations. email: [email protected] email: [email protected]

Both particle physics and all the approaches to gravity make use of variational principles employing singular Lagrangians [1]. As a consequence the Euler-Lagrange equations cannot be put in normal form, some of them may be non independent equations (due to the contracted Bianchi identities) and a subset of the original configuration variables are left completely or partially indetermined. Moreo...

This article describes the design, modeling and identification of the main hydrodynamic parameters of an underwater glider vehicle is presented. The equations describing the dynamics of the vehicle is obtained from the Euler-Lagrange method. The main hydrodynamic parameters were obtained considering the geometry of the vehicle and its operating characteristics. Finally, simulation open loop sys...

We study Euler–Poincaré systems (i.e., the Lagrangian analogue of LiePoisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincaré equations for a parameter dependent Lagrangian by using a variational principle of Lagrange d’Alembert type. Then we derive an abstract Kelvin-Noether theorem for these equations. We also explore their rela...

This paper is concerned with comparing Newtonian and Lagrangian methods in Mechanics for determining the governing equations of motion (usually called Euler-Lagrange equations) for a collection of deformable bodies immersed in an incompressible, inviscid fluid whose flow is irrotational. The bodies can modify their shapes under the action of inner forces and torques and are endowed with thruste...