Composition of rotations and parallel transport

Nonlinearity

Volumn 9, Issue 2, 1996, Pages 413-419

  Levi, Mark ^a  

^a Rensselaer Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22244458930     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/9/2/007     Document Type: Article

References (18)

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3. Berry M V 1984 Quantal phase factors accompanying adiabatic changes Proc. R. Soc. A 392 45-57
4. Bloch A, Krishnaprasad P S, Marsden J and Sanchez-Alvarez 1996 Stability of rigid body dynamics by internal and external torques Automatica in press
5. Chicone C 1990 Bifurcations of nonlinear oscillations and frequency entrainment near resonance Preprint
6. Diliberto S I 1950 On systems of ordinary differential equations, Contributions to the theory of Nonlinear Oscillations (Ann. Math. Stud.) 20 (Princeton, NJ: Princeton University Press)
7. DoCarmo M P 1976 Differential Geometry of Curves and Surfaces (Englewood Cliffs, NJ: Prentice Hall)
8. Hannay J H 1985 Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian J. Phys. A: Math. Gen. 18 221-30
9. Levi M 1994 A 'bicycle wheel' proof of the Gauss-Bonnet theorem, dual cones and some mechanical manifestations of the Berry phase Expo. Math. 12 145-64
10. Levi M 1993 Geometric phases in the motion of rigid bodies Arch. Rat. Mech. Anal. 122 213-29
11. Levi M 1993 A theorem of Poinsot, path ordered integrals and parallel transport Fields Insitute Communications vol 1 133-8
12. Marsden J 1992 Lecture Notes on Mechanics (London Math. Soc. Lect. Notes Series 174) (Cambridge: Cambridge University Press)
13. Marsden J, Montgomery R and Ratiu T 1990 Reduction, symmetry and Berry's phase in mechanics Mem. AMS 88
14. Montgomery R 1988 The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case Commun. Math. Phys. 120 269-94
15. Montgomery R 1991 By how much does the rigid body rotate? A Berry's phase from the 18th century Am. J. Phys. 59
16. Shapere A and Wilczek F 1989 Geometric Phases in Physics (Singapore: World Scientific)
17. Simon B 1983 Holonomy, the quantum adiabatic theorem and Berry's phase Phys. Rev. Lett. 5 2167-70
18. Whittaker E T 1988 A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge: Cambridge University Press)