Authors: Zinkevych Ya.S.
In this article a minimum-time problem of deceleration of rotations of a free rigid body is studied analytically and numerically. It is assumed that a body contains a spherical cavity filled with highly viscous fluid. The body is subjected to a retarding torque of viscous friction. It is assumed that such body is dynamically asymmetric. An optimal control law for deceleration of rotations of the body is synthesized, and the corresponding time and phase trajectories are determined.
The asymptotic approach made it possible to determine the control evolutions of the magnitude squared of the elliptic functions modulus k2, dimensionless kinetic energy and kinetic moment. The qualitative properties of the optimal motion were also found.
The obtained results allow us to build a synthesis of the optimal deceleration of rotations of satellites and spacecrafts. They can be used to analyze dynamics of controlled spacecrafts.
Tags: asymmetric body; cavity; optimal deceleration; resistive medium
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