43 citations · 352 across the 38 of their papers we have counts for
35 papers
The Cartan-Kähler theorem for exterior differential systems on transitive Lie algebroids
Sonja Hohloch, Tom Mestdag, Kenzo Yasaka
The notion of an exterior differential system (on a manifold) has recently been extended to the setting of a Lie algebroid. Here, we further develop the theory and we present two v…
Projective geodesic extensions by conformal modifications in nonholonomic mechanics
Malika Belrhazi, Tom Mestdag
Projective geodesic extensions are reparametrizations of the trajectories of a nonholonomic mechanical system (with only a kinetic energy Lagrangian), in such a way that they can b…
Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations
Tom Mestdag, Kenzo Yasaka
We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of su…
Geodesic extensions of mechanical systems with nonholonomic constraints
Malika Belrhazi, Tom Mestdag
For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a…
Conditions for symmetry reduction of polysymplectic and polycosymplectic structures
Eduardo García-Toraño Andrés, Tom Mestdag
For Hamiltonian field theories on polysymplectic manifolds with a symmetry group action and a momentum map, we explore the redundancy in a set of necessary conditions that has appe…
Cotangent bundle reduction and Routh reduction for polysymplectic manifolds
Santiago Capriotti, Viviana Alejandra Díaz, Eduardo García-Toraño Andrés +1
We discuss Lagrangian and Hamiltonian field theories that are invariant under a symmetry group. We apply the polysymplectic reduction theorem for both types of field equations and…