Momentum Transfer in Torque-Free Gyrostats

Abstract

The rotational dynamics of gyrostats containing N axisymmettic rotors are studied, with special attention to the transfer of angular momentum which occurs when spinup torques are applied to the rotors by motors on the platform. This work has relevance to orientational maneuvers of artificial satellites, such as pointing of the Hubble Space Telescope. The rotational dynamics are described by TV + 3 firstorder differential equations, which are partially put into noncanonical Hamiltonian form. The equations are integrable in case the spinup torques are all zero or if the spinup torques are such that the rotors all have constant angular momentum relative to a body-fixed frame. Conservation of angular momentum and the method of averaging are used to reduce the number of equations of motion to one for the case of small constant spinup torques. The corresponding geometric reduction to a planar slow state space is useful for studying and planning momentum transfer maneuvers. This reduction is formally valid only in regions of phase space where the unperturbed motion is periodic. The neighborhood of the unperturbed separatrices are therefore regions where averaging fails to describe the motion adequately, and are also indicative of dramatic changes in the attitude dynamics. Exact solutions to the averaged equations are used to justify further the projection of solutions of the exact system onto the slow state space. The slow state space is used to illuminate two interesting momentum transfer phenomena.Nonlinear Dynamics Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 10/04/15. For personal use only.

Double averaging approach to the study of spinup dynamics of flexible satellites

“…10 Let 0(y,t) be the rotation of the beam relative to the xyz axes and assume that the rotation of the continuous beam can be replaced by a series of generalized coordinates in time and admissible functions in space, such as (6) so the equations can be converted into ordinary differential equations in time only. The rotation that the tip mass experiences is simply Eq.…”

“…The general problem of spinup of axial gyrostats with platform asymmetry was studied by Hall and Rand, 4 and spinup of more general gyrostats was studied by Hall. 5 - 6 The addition of flexible appendages to gyrostats has been studied by numerous authors; a comprehensive review of early work was done by Modi. 7 The model used in this paper consists of a rigid platform and rotor with a flexible appendage whose vibrations are constrained to purely torsional modes (e.g., constrained by guy wires).…”