Hostname: page-component-7bb8b95d7b-dtkg6 Total loading time: 0 Render date: 2024-09-25T11:22:14.818Z Has data issue: false hasContentIssue false
  • English
  • Français

Gyrostats in free Rotation

Published online by Cambridge University Press:  12 April 2016

Antonio Elipe
Antonio Elipe*
Affiliation:
Grupo de Mecánica Espacial, Universidad de Zaragoza Zaragoza, Spain

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
International Astronomical Union Colloquium , Volume 165: Dynamics and Astrometry of Natural and Artificial Celestial Bodies , 1997 , pp. 391 - 398
Copyright
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
Hughes, P.C.: 1986, Spacecraft Attitude Dynamics, John Wiley & Sons.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