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Gyrostats in free Rotation
Published online by Cambridge University Press: 12 April 2016
Abstract
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We consider the problem of the attitude dynamics of a gyrostat under no external torques and constant internal spins. We introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere. This new representation shows that the problem is a particular case in the class of dynamical systems defined by a Hamiltonian that is a polynomial of at most degree two in a base of the Lie algebra so(3).
- Type
- Theory of Motion
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- Copyright © Kluwer 1997
References
Chiang, R.C.: 1995, “Effects of an internal angular momentum on the rotation of a symmetrical top”, J. Math. Phys.
36, 3345–3352.CrossRefGoogle Scholar
Cochran, J.E., Shu, P.H., and Rews, S.D.: 1982, “Attitude motion of asymmetric dual-spin spacecraft”, J. Guid. Contr. Dyn.
5, 37–42.CrossRefGoogle Scholar
Deprit, A. and Elipe, A.: 1993, “Complete reduction of the Euler-Poinsot problem”, J. Astronaut. Sci.
41, 603–628.Google Scholar
Elipe, A. and Lanchares, V.: 1994, “Biparametric quadratic Hamiltonians on the unit sphere: complete classification”, Mech. Res. Comm.
21, 209–214.CrossRefGoogle Scholar
Frauendiener, J.: 1995, “Quadratic Hamiltonians on the unit sphere”, Mech. Res. Comm.
22, 313–317.CrossRefGoogle Scholar
Hall, C.D. and Rand, R.H.: 1994, “Spinup dynamics of axial dual-spin spacecraft”, J. Guid. Contr. Dyn.
17, 30–37.CrossRefGoogle Scholar
Hall, C.D.: 1995 “Spinup dynamics of biaxialgyrostats”, J. Astronaut. Sci.
43, 263–275.Google Scholar
Lanchares, V.: 1993, “Sistemas dinámicos bajo la acción del grupo SO(3): El caso de un Hamiltoniano cuadrático”, Ph. D. dissertation, Pub. Sem. Mat. García Galdeano II, 44 (University of Zaragoza).Google Scholar
Lanchares, V. and Elipe, A.: 1995, “Bifurcations in biparametric quadratic potentials”, Chaos
5, 367–373.Google Scholar
Lanchares, V. and Elipe, A.: 1995, “Bifurcations in biparametric quadratic potentials, II”, Chaos
5, 531–535.Google Scholar
Lanchares, V., et al.: 1995, “Surfaces of bifurcation in a triparametric quadratic Hamiltonian”, Phys. Rev.
E52, 5540–5548.Google Scholar
Leimanis, E.: 1965, The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point, Springer, Heidelberg.CrossRefGoogle Scholar
Poinsot, L.: 1851, “Theorie nouvelle de la rotation des corps”, J. Math. Pures Appl.
16, 289–336.Google Scholar
Tong, X., Tabarrok, B., and Rimrott, F.P.J.: 1995, “Chaotic motion of an asymmetric gyrostat in the gravitational field”, Int. J. Non-Linear Mech.
30, 191–203.CrossRefGoogle Scholar
Volterra, V.: 1899, “Sur la théorie des variations des latitudes”, Acta Math.
22, 201–358.Google Scholar