Related papers: Lagrangian Dynamics on Matched Pairs
For the Jordan algebra of hermitian matrices of order $n\ge 2$, we let $X$ be its submanifold consisting of rank-one semi-positive definite elements. The composition of the cotangent bundle map $\pi_X$: $T^*X\to X$ with the canonical map…
The Helmholtz conditions are necessary and sufficient conditions for a system of second order differential equations to be variational, that is, equivalent to a system of Euler-Lagrange equations for a regular Lagrangian. On the other hand,…
In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…
We prove that the tangent bundle of a generic space of planar n-gons with specified side lengths, identified under isometry, plus a trivial line bundle is isomorphic to (n-2) times a canonical line bundle. We then discuss consequences for…
The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…
We consider smooth families of Lie groups (group bundles) and connections that are compatible with the group operation. We characterize the space of group connections on a group bundle as an affine space modeled over the vector space of…
We establish a "matrix simultaneous diagonalization theorem" for disconnected reductive groups which relaxes both the semisimplicity condition and the commutativity condition. As an application, we prove the following basic results…
This paper surveys various results concerning stability for the dynamics of Lagrangian (or Hamiltonian) systems on compact manifolds. The main, positive results state, roughly, that if the configuration manifold carries a hyperbolic metric,…
Manifolds with a commutative and associative multiplication on the tangent bundle are called F-manifolds if a unit field exists and the multiplication satisfies a natural integrability condition. They are studied here. They are closely…
The application of a gauge covariant derivative to the Euler-Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic…
We analyze the correspondence between finite sequences of finitely supported probability distributions and finite-dimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on…
The theory of perfect fluids is reconsidered from the point of view of a covariant Lagrangian theory. It has been shown that the Euler-Lagrange equations for a perfect fluid could be found in spaces with affine connections and metrics from…
We provide a quasi-Poisson version of the Drinfeld's correspondence between Poisson homogeneous spaces and Lagrangian subalgebras.
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…
We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a…
We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to…
The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented. Some applications are given; in particular, a geometric…
We consider a generalization of nonrelativistic Schr\"odinger-Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and…
We characterize Kaehler manifolds with trivial logarithmic tangent bundle (with respect to a divisor D) as a class of certain compatifications of complex semi-tori.
The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…