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Geometric Analysis of Noisy Perturbations to Nonholonomic Constraints

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Stochastic Geometric Mechanics (CIB-SGM 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 202))

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Abstract

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 .

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Acknowledgements

We acknowledge fruitful and enlightening discussions with Profs. M. Barlow, L. Bates, A. M. Bloch, D. D. Holm, G. Pavliotis, T. S. Ratiu, J. Sniatycki, and D. V. Zenkov. FGB is partially supported by the ANR project GEOMFLUID 14-CE23-0002-01. VP acknowledges support from NSERC Discovery Grant and the University of Alberta Centennial Fund.

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Authors and Affiliations

  1. LMD/IPSL, CNRS, Ecole Normale Supérieure, PSL Research University, Ecole Polytechnique, Université Paris-Saclay, Sorbonne Universités, UPMC Univ Paris 06, 24 Rue Lhomond, 75005, Paris, France

    François Gay-Balmaz

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Vakhtang Putkaradze

Authors
  1. François Gay-Balmaz
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  2. Vakhtang Putkaradze
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Corresponding author

Correspondence to François Gay-Balmaz .

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Editors and Affiliations

  1. Institute of Applied Mathematics and HCM, University of Bonn, Bonn, Germany

    Sergio Albeverio

  2. Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    Ana Bela Cruzeiro

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Darryl Holm

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Gay-Balmaz, F., Putkaradze, V. (2017). Geometric Analysis of Noisy Perturbations to Nonholonomic Constraints. In: Albeverio, S., Cruzeiro, A., Holm, D. (eds) Stochastic Geometric Mechanics . CIB-SGM 2015. Springer Proceedings in Mathematics & Statistics, vol 202. Springer, Cham. https://doi.org/10.1007/978-3-319-63453-1_4

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