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Geometric mechanics on nonholonomic submanifolds

Olga Krupková (2010)

Communications in Mathematics

In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical systems subject...

Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure

Šilhánek, David, Beneš, Michal (2023)

Programs and Algorithms of Numerical Mathematics

In the present contribution we discuss mathematical homogenization and numerical solution of the elliptic problem describing convection-diffusion processes in a material with fine periodic structure. Transport processes such as heat conduction or transport of contaminants through porous media are typically associated with convection-diffusion equations. It is well known that the application of the classical Galerkin finite element method is inappropriate in this case since the discrete solution...

Several examples of nonholonomic mechanical systems

Martin Swaczyna (2011)

Communications in Mathematics

A unified geometric approach to nonholonomic constrained mechanical systems is applied to several concrete problems from the classical mechanics of particles and rigid bodies. In every of these examples the given constraint conditions are analysed, a corresponding constraint submanifold in the phase space is considered, the corresponding constrained mechanical system is modelled on the constraint submanifold, the reduced equations of motion of this system (i.e. equations of motion defined on the...

Taylor obstruction to the integrability of homogeneous potentials of degree two. An application of higher order variational equations

Guillaume Duval, Andrzej J. Maciejewski (2011)

Banach Center Publications

We show how using the differential Galois theory one can find effectively necessary conditions for the integrability of Hamiltonian systems with homogeneous potentials.

The origin of variational principles

Włodzimierz M. Tulczyjew (2003)