TY - GEN
T1 - Variational Principle for Stochastic Nonholonomic Systems Part I
T2 - 7th International Conference on Geometric Science of Information, GSI 2025
AU - Li, Tianzhi
AU - Gay-Balmaz, François
AU - Shi, Donghua
AU - Wang, Jinzhi
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.
PY - 2026
Y1 - 2026
N2 - Nonholonomic mechanics has received considerable attention in dynamics and control area. However, due to a wide range of fluctuations in the physical world, the ideal mathematical models of mechanical systems with nonholonomic constraints suffer from issues of ignoring the real-world perturbations and physically difficult to realize. Motivated by recent developments in stochastic and constrained mechanics, here we present a stochastic variational formulation for mechanical systems with or without stochastic nonholonomic constraints. We give stochastic variational principles for both stochastically unconstrained and nonholonomic cases under the same framework by deriving the stochastic implicit Hamel equations. Moreover, an interesting example of the stochastic rolling disk is provided to illustrate the proposed method.
AB - Nonholonomic mechanics has received considerable attention in dynamics and control area. However, due to a wide range of fluctuations in the physical world, the ideal mathematical models of mechanical systems with nonholonomic constraints suffer from issues of ignoring the real-world perturbations and physically difficult to realize. Motivated by recent developments in stochastic and constrained mechanics, here we present a stochastic variational formulation for mechanical systems with or without stochastic nonholonomic constraints. We give stochastic variational principles for both stochastically unconstrained and nonholonomic cases under the same framework by deriving the stochastic implicit Hamel equations. Moreover, an interesting example of the stochastic rolling disk is provided to illustrate the proposed method.
KW - Hamel’s formalism
KW - Noisy constraints
KW - Stochastic nonholonomic mechanics
KW - Variational principle
UR - https://www.scopus.com/pages/publications/105035291201
U2 - 10.1007/978-3-032-03921-7_21
DO - 10.1007/978-3-032-03921-7_21
M3 - Conference contribution
AN - SCOPUS:105035291201
SN - 9783032039200
T3 - Lecture Notes in Computer Science
SP - 204
EP - 213
BT - Geometric Science of Information - 7th International Conference, GSI 2025, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 29 October 2025 through 31 October 2025
ER -