Escape from Gyrostat Trap States

Abstract

Some results are presented on the dynamics of gyrostats containing two axisymmetric rotors where one of the rotors is viscously damped and the other is subject to a controllable torque. The purpose of this arrangement is to investigate the use of internal torques to enable a spacecraft to escape from a trap state. Suppose the spacecraft is intended to operate in a state in which the primary rotor R 1 has a speci ed angular momentum and the other rotor R 2 , subject only to internal viscous torques, is not spinning relative to the spacecraft reference frame. Normally this state is asymptotically stable because of the damping. It is possible that a different asymptotically stable state exists satisfying these conditions on the rotor momenta, in much the same way that a single-spinner may spin in either direction about its major axis. If the spacecraft becomes trapped in the alternate state, it is necessary to help it escape. In an earlier study, a pulsing procedure was proposed. Herein we show that periodic torquing of the primary rotor may lead to escape but generally is rather ineffective. An alternative escape procedure is presented that essentially is guaranteed to lead to escape. Unlike the local analysis that suggests the pulsing procedure, the procedure used here is based on a global analysis of the rotational dynamics.

Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems

“…Motion equations (4) and (6) corresponding to the spider with six rotors can be generalized for description of attitude dynamics of rotor-type spider with 6N rotors ( Fig.1-b). As presented in Fig.1-b multirotor system has got N rotors on every ray -N rotor layers (levels).…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. This paper sets out to develop a new multiple-rotor system, which also can be used for attitude control of a SC.…”

Behavior of a Free Dual-Spin Gyrostat with Different Ratios of Inertia Moments

“…Furthermore, Kane [2] has given the solution for the attitude motion of an axial gyrostat with a driven rotor. In many papers (see, e.g., [3][4][5][6][7][8][9][10][11][12][13][14][15][16]), this modern problem is usually performed by following two distinct steps. The dynamics of the rotation are represented by using differential equations written for the components of the angular momentum, and then the kinematic equations are utilized to transform the angular momentum.…”

“…Hall [6] proposed a procedure based upon the global analysis of the rotational dynamics. Hall and Rand [7] considered spinup dynamics of classical axial gyrostat composed of an asymmetric platform and an axisymmetric rotor.…”