Two-Impulse Reorientation of Spinning Axisymmetric Body: Single Axis Thrust
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o-Impulse Reorientation of Spinning Axisymmetric Body: Single Axis Thrust Neha Satak,1 Jeremy J. Davis,1 James Doebbler,1 and John E. Hurtado2
Abstract It is well known that a sequence of two impulses can be used to redirect the spin axis of an axisymmetric rigid body. The first impulse initiates the coning motion by imparting an initial transverse component of angular velocity. The second impulse brings the coning motion to a halt by completely canceling the transverse angular velocity. When the torque can be given along only one axis in the transverse plane then a two-impulse maneuver can be designed with a coast time before the initiation of the maneuver. The coast time is required to align the torque axis in a specific direction. Further, by appropriately choosing the time of the second impulse, a solution is found when the impulse is restricted to only one direction along a single axis.
Introduction The problem of reorienting the spin axis of a rigid body has been studied extensively. An axisymmetric body is a special case of a general rigid body with an axis of symmetry. Most spinning satellites and other spinning rigid bodies are designed or can be idealized to be axisymmetric; therefore, it is beneficial to study this special case. To reorient the axisymmetric body, impulse based controls [1, 2, 3] and continuous controls [4, 5, 6, 7, 8] have been designed. An open loop two-impulse scheme for reorienting the axisymmetric spinning body was developed by Grubin [1]. In that scheme, the initial impulse makes the body precess in the direction of the desired attitude and the second impulse stops the precession. In his work, he assumed that two impulsive controls spanning the complete transverse plane of the body are available. In this present work, a two impulse-solution is found for the case when only one body-fixed impulsive control in the transverse plane is available. A fuel optimal two-impulse solution for the case when the applied thrust is finite was found by Porcelli and Connolly [2]. Their technique is graphical and uses a 1
Graduate Student, Department of Aerospace Engineering, Texas A&M University, College Station, USA. Associate Professor, Department of Aerospace Engineering, Texas A&M University, College Station, USA.
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simplified mathematical model of the spinning rigid body. Redmond and Silverberg [3] used an adaptive grid bisection search to compute the fuel optimal impulsive reorientation maneuver for small and large maneuver times. They concluded that for a large enough maneuver time their technique results in the two-impulse maneuver whereas for an even larger maneuver time, a multipleimpulse solution is more fuel optimal. In the present paper, it is shown that for the restricted impulse direction case the minimum fuel two-impulse solution can be easily found when the maneuver time and the required fuel are finite. A sequential algorithm to find the minimum time solution is also given in this paper. Though continuous controllers are not discussed in this paper, reori
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