Parabolic geometry of a car

Lundi 6 mai 14:00-15:00 - Pawel Nurowski - Center for Theoretical Physics, Polish Academy of Sciences

Résumé : I will discuss the geometry of the configuration space of a car equipped with ideal tires. Such a physical system is nonholonomic, meaning that its velocities obey constraints that can not be integrated to the constraints on positions. These constraints are linear, which results in equipping the configuration space of a car with the structure of a bracket generating vector
distribution. Surprisingly, two kinds of very natural movements of a car define an additional structure on this distribution, whose local symmetry is SO(2,3).
My talk will try to provide elementary arguments why this simple Lie group, which in particular is a conformal symmetry group of the 3-dimensional Minkowski space, appears as one of the features of any car.

Lieu : IMO ; salle 3L8.

Parabolic geometry of a car  Version PDF