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Reduction, symmetry, and phases in mechanics


About this Title

J. Marsden, R. Montgomery and T. Ratiu

Publication: Memoirs of the American Mathematical Society
Publication Year 1990: Volume 88, Number 436
ISBNs: 978-0-8218-2498-6 (print); 978-1-4704-0859-6 (online)
DOI: http://dx.doi.org/10.1090/memo/0436
MathSciNet review: 1030714
MSC (1991): Primary 58F05; Secondary 58F35, 70G35, 70H05, 81Q99

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Table of Contents


Chapters

  • 1. Some examples
  • 2. Reconstruction of dynamics for Hamiltonian systems
  • 3. Reconstruction of dynamics for Lagrangian systems
  • 4. Ehresmann connections and holonomy
  • 5. Reconstruction phases
  • 6. Averaging connections
  • 7. Existence, uniqueness and curvature of the Hannay-Berry connections
  • 8. The Hannay-Berry connection in the presence of additional symmetry
  • 9. The Hannay-Berry connection on level sets of the momentum map
  • 10. Case I: Bundles of symplectic manifolds with the canonical connection; integrable systems
  • 11. Case II: Cartan connections; moving systems
  • 12. The Cartan angles; the ball in the hoop and the Foucault pendulum
  • 13. Induced connections on the tower of bundles
  • 14. The Hannay-Berry connection for general systems