43 citations · 352 across the 38 of their papers we have counts for
27 papers · 1 filter
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…
Homogeneous nonlinear splittings and Finsler submersions
S. Hajdu, T. Mestdag
A nonlinear splitting on a fibre bundle is a generalization of an Ehresmann connection. An example is given by the homogeneous nonlinear splitting of a Finsler function on the tota…
Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations
W. Sarlet, T. Mestdag
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear tra…