The dynamics of a dual-spinner subject to the action of an internal oscillatory torque and Coulomb friction between the two linked bodies is investigated. The conditions for existence of transverse homoclinic points and homoclinic tangency of chaotic motions are obtained using Melnikov’s method. Through long-term numerical integration of the equations of motion, steady-state chaotic attractors are also found and studied numerically by varying the forcing amplitude.
Issue Section:
Technical Papers
1.
Danby, J. M., 1962, Fundamentals of celestial mechanics, Macmillan, New York.
2.
Guckenheimer, J., and Holmes, P., 1983, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer-Verlag, New York.
3.
Hall
C. D.
Rand
R. H.
1994
, “Spinup Dynamics of Axial Dual-Spin Spacecraft
,” J. Guidance, Control, and Dynamics
, Vol. 17
, No. 1
, pp. 30
–37
.4.
Holmes
P. J.
Whidey
D. C.
1983
, “On the Attracting Set for Duffing’s Equation, II. A Geometrical Model for Moderate Force and Damping
,” Physica
, Vol. 7D
, pp. 111
–123
.5.
Huberman
B. A.
Crutchfield
J. P.
1979
, “Chaotic States of Anharmonic Systems in Periodic Fields
,” Phys. Rev. Lett.
, Vol. 43
, pp. 1743
–1747
.6.
Hughes, P. C., 1986, Spacecraft Attitude Dynamics, John Wiley and Sons, New York.
7.
Lichtenberg, A. J., and Lieberman, M. A., 1983, Regular and stochastic motion, Springer-Verlag, New York.
8.
Lorenz
E. N.
1963
, “Deterministic Nonperiodic Flow
,” J. Atmos. Sci.
, Vol. 20
, pp. 130
–141
.9.
Masaitis
C.
1961
, “On the Motion of Two Linked Bodies
,” Archive for Rational Mechanics and Analysis
, Vol. 8
, No. 1
, pp. 23
–35
.10.
Moon
F. C.
Holmes
P. J.
1979
, “A Magnetoelastic Strange Attractor
,” J. Sound Vib.
, Vol. 65
, No. 2
, pp. 285
–296
.11.
Scher
M. P.
Farrenkopf
R. L.
1974
, “Dynamic Trap States of Dual Spin Spacecraft
,” AIAA Journal
, Vol. 12
, No. 12
, pp. 1721
–1725
.12.
Ueda, Y., 1980, “Explosion of strange attractors exibitited by Duffing’s Equation,” Nonlinear Dynamics, R. H. G. Helleman, ed., New York Academy of Sciences, New York, pp. 422–434.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.