Dynamics of non-holonomic systems with stochastic transport.
Proc Math Phys Eng Sci
; 474(2209): 20170479, 2018 Jan.
Article
in En
| MEDLINE
| ID: mdl-29434503
ABSTRACT
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Language:
En
Journal:
Proc Math Phys Eng Sci
Year:
2018
Document type:
Article
Affiliation country:
United kingdom