The Project:

*Numerical simulation of nonholonomic mechanical systems*

Nonholonomic
mechanical systems are of great interest in robot technologyapplications and
control, in particular robotic locomotion and robotic grasping. Roughly
speaking a mechanical system with nonholonomic constraints is described by a
constrained di erential equation (in Lagrangian or Hamiltonian form) such that
the constrains are involving the velocity of the system and not only the
positions. In this project the numerical simulation of some simple noholonomic
mechanical systems will be considered. Possible examples are a vertical disk
rolling on a plane, gure 2, a nonholonomically constrained particle in
R3,
a ball on a spinning plate, the snake-board (a variant of the skate-board),
gure 1. The aim of the project is understanding the basic theoretical features
of nonholonomically constrained systems, illustrate them via numerical
simulation, and discuss which numerical approaches are best suited for such
problems. In particular classical Runge-Kutta methods will be rst applied to
the problems and then more specic geometric integrators will be also used. A
comparison of the performance of the methods will be part of the presented
results.

Figure 1: The
snake-board.

Figure 2: The rolling disk