WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 12, 2013
Exact Solutions in Attitude Dynamics of a Magnetic Dual-Spin Spacecraft and a Generalization of the Lagrange Top
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Abstract: The present paper contains an investigation results for the attitude motion of a magnetic dual-spin spacecraft (DSSC) in the geomagnetic field at the realization of the orbital motion of its mass center along an equatorial circular orbit. Exact analytical solutions for the attitude motion parameters are obtained in the elliptic Jacobi functions including the angular momentum components, the directional cosines and the Euler angles. These analytical exact solutions correspond to generating dependences which make possible the advanced research of the DSSC perturbed motion cases. The considering task of the DSSC angular motion can be characterized as the Lagrange top generalization for the coaxial bodies system – the corresponding case of the magnetic DSSC motion occurs under the influence of external restoring/overturning torques (like in the Lagrange heavy top motion). This paper’s results also can be directly reduced to the Euler coaxial top’s (Euler’s case of the rigid body and coaxial bodies motion) general exact explicit solutions; this circumstance can be consider as a generalization of the Euler coaxial top’s problem. An important “dynamical equivalence” between the magnetic and gyroscopic DSSC attitude stabilization factors is illustrated.
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Keywords: Magnetic Dual-Spin Spacecraft, Explicit Solutions, Jacobi Functions, Lagrange top, Euler top