9 results found
Ribeiro Castro A, 2017, Noise and dissipation in rigid body motion, Publisher: Springer
Using the rigid body as an example, we illustrate some features of stochastic geometric mechanics. These features include: (i) a geometric variational motivation for the noise structure involving Lie-Poisson brackets and momentum maps , (ii) stochastic coadjoint motion with double bracket dissipation , (iii) description and its stationary solutions , (iv) random dynamical systems , random attractors and SRB measures connected to statistical physics.
Arnaudon A, De Castro AL, Holm D, 2017, Noise and Dissipation on Coadjoint Orbits, Journal of Nonlinear Science, Vol: 28, Pages: 91-145, ISSN: 0938-8974
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect product extension. Random attractors are found for this general class of systems when the Lie algebra is semi-simple, provided the top Lyapunov exponent is positive. We study in details two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown.
Castro A, Howard W, Shanbrom C, 2017, Complete spelling rules for the Monster tower over three-space, Journal of Geometric Mechanics, Vol: 9, Pages: 317-333, ISSN: 1941-4897
Shanbrom C, Howard W, Castro AL, 2015, Bridges between subriemannian geometry and algebraic geometry: Now and then, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain), Publisher: American Institute of Mathematical Sciences
Castro AL, Howard WC, 2013, A Semple-type approach to a problem of Goursat: The multi-flag case, Comptes Rendus Mathematique, Vol: 351, Pages: 921-925, ISSN: 1631-073X
Castro AL, Montgomery R, 2012, Spatial curve singularities and the monster/semple tower, Israel Journal of Mathematics, Vol: 192, Pages: 381-427, ISSN: 0021-2172
Castro A, Montgomery R, 2008, The chains of left-invariant Cauchy–Riemann structures on SU(2), Pacific Journal of Mathematics, Vol: 238, Pages: 41-71, ISSN: 0030-8730
Shi X, Ribeiro Castro AL, Manduchi R, et al., 2006, Rotational Invariant Operators Based on Steerable Filter Banks, IEEE Signal Processing Letters, Vol: 13, Pages: 684-687, ISSN: 1070-9908
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.