TY - GEN
T1 - Geometric analysis of noisy perturbations to nonholonomic constraints
AU - Gay-Balmaz, François
AU - Putkaradze, Vakhtang
N1 - Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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.
AB - 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.
KW - Nonholonomic systems
KW - Stochastic constraints
KW - Suslov problem
U2 - 10.1007/978-3-319-63453-1_4
DO - 10.1007/978-3-319-63453-1_4
M3 - Conference contribution
AN - SCOPUS:85035082045
SN - 9783319634524
T3 - Springer Proceedings in Mathematics and Statistics
SP - 57
EP - 75
BT - Stochastic Geometric Mechanics
A2 - Albeverio, Sergio
A2 - Cruzeiro, Ana Bela
A2 - Holm, Darryl
PB - Springer New York LLC
T2 - Workshop on Classic and Stochastic Geometric Mechanics, CIB-SGM 2015
Y2 - 8 June 2015 through 11 June 2015
ER -