Paweł Nurowski (CTP PAS): Simple nonholonomic systems on the plane. Lecture 1
Channel: Centrum Fizyki Teoretycznej PAN
Date: 16/09/2021

Paweł Nurowski (CTP PAS).
Simple nonholonomic systems on the plane. Lecture 1.
The purpose of this lecture is to give an introduction for studies of geometries of mechanical systems obeying nonholonomic constraints. Such notions as configuration space, nonholonomic constraints - linear or nonlinear, vector distributions, their ranks and growth vectors, will be introduced. I will also introduce the notion of a bracket generating distribution and the velocity distribution of a mechanical system. The problem of achievability will be mentioned: Chow-Raszewski and Nagano-Sussman theorems, giving necessary and sufficient conditions for the system obeying nonholonomic constraints to achieve any point in the configuration space, will be stated. The symmetries of mechanical systems with nonholonomic constraints will be defined and studied. All the notions will be illustrated on an example of the mechanical system of a skate blade moving without skidding on an ice rink. I  will end up the part one of the lecture with a question if a given manifold, with a bracket generating vector distribution on it, can be realized as a configuration space, and respectively, velocity distribution of a nonholonomic mechanical system.

GRIEG collaboration project: SCREAM workshop 2021.