Pointing accuracy of a dual-spin satellite due to torsional appendage vibrations

Abstract

This paper deals with the attitude motion of a dual-spin satellite with a finite sized rigid body attached to the end of a flexible beam. The equations of motion are derived using Lagrange's equations and are solved using the perturbation technique known as the Krylov-Bogoliubov-Mitropolsky method. The special case of torsional flexibility is presented in its entirety. The relationships between the satellite, beam and tip mass parameters, and pointing accuracy of the satellite are examined.

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

“…where u> 2 = cos# -<w z sin0), [a> y + 6(L,t)] 9 (co z cos# -co x sin 0)} is the angular velocity of the tip mass expressed in terms of principal coordinates of the tip mass, and/ 2 = diag[/ x , I y , I z ] is the principal inertia tensor of the tip mass about c 2 . It is also diagonal relative to the xyz frame in the undeformed case.…”

“…Note that the method of averaging is applied twice in this process, first in order to obtain the T = 0 solution from Ref. 9 and then to obtain the slow evolution of energy (as in this work). In each case, a small parameter is available to justify the use of the averaging approximation.…”

“…This requires a known periodic T = 0 solution that is taken from Ref. 9, wherein the Krylov-Bogoliubov-Mitropolski (KBM) averaging method 10 is applied to a dual-spin spacecraft with a flexible appendage and zero spinup torque applied to the rotor. Note that the method of averaging is applied twice in this process, first in order to obtain the T = 0 solution from Ref.…”

“…Our approach is based on the approximate zero torque solution developed in Ref. 9 and uses the averaging approach developed for small torque in Ref. 4.…”