22 research outputs found
Geometric analysis of noisy perturbations to nonholonomic constraints
We propose two types of stochastic extensions of nonholonomic constraints for
mechanical systems. Our approach relies on a stochastic extension of the
Lagrange-d'Alembert framework. We consider in details the case of invariant
nonholonomic systems on the group of rotations and on the special Euclidean
group. Based on this, we then develop two types of stochastic deformations of
the Suslov problem and study the possibility of extending to the stochastic
case the preservation of some of its integrals of motion such as the Kharlamova
or Clebsch-Tisserand integrals
Residual Finiteness Growths of Virtually Special Groups
Let be a virtually special group. Then the residual finiteness growth of
is at most linear. This result cannot be found by embedding into a
special linear group. Indeed, the special linear group
, for , has residual finiteness growth
.Comment: Updated version contains minor changes incorporating referee
comments/suggestions and a simplified proof of Lemma 4.