Minimum energy trap states of dual-spin spacecraft

Hollars, Michael G.

doi:10.2514/6.1980-1780

Cited by 2 publications

(1 citation statement)

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“…This kind of minimum energy trap state was further studied by Hollars. 5 In a dual spinner, the platform is not distinguished from the rotor, except for the direction of spin angular momentum flux; it is conjectured that an unbalanced rotor might also cause the resonance. Lebsock et al 6 studied the latter possibility and found yet another type of resonance, which they called the unitary inertia ratio resonance.…”

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confidence: 99%

Resonances in the despin dynamics of dual-spin spacecraft

1991

Journal of Guidance, Control, and Dynamics

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A unifying treatment of the nutation resonances encountered during the despin of platform of a dual-spin spacecraft with transverse inertia asymmetry and either platform or rotor imbalance is developed. The linear model equations governing the resonance dynamics depend on three nondimensional parameters that measure the degree of dynamic imbalance, asymmetry, and the time duration available for resonance growth. The solution dependence on all of these parameters is studied, and the basic physics of the phenomena is emphasized. The linear theory is supplemented by a simple variational analysis that provides a phase plane geometric interpretation of a rather interesting saddle-type transition, which has been observed in fully nonlinear simulations. The transition leads to an abrupt change in the spin orientation commonly known as the "stall" in spacecraft despin maneuvers. NomenclatureH = angular momentum vector of the system H = magnitude of H H 3 = spin component of H ///*> = angular momentum component, x = n: nonresonant body; x = r: resonant body; i = 1,2,3 // = /th component total transverse moment of inertia, i = 1,2 / 3 = rotor moment of inertia, spin component /f = platform moment of inertia, spin component /i 3 = rotor product of inertia 7f 3 = platform product of inertia //** = moment of inertia referring to system reference frame, x -n: nonresonant body; x = r: resonant body;/= 1,2,3 '/£) = product of inertia, x = n: nonresonant body; x = r: resonant body; i = 1,2,3 I t = averaged total transverse moment of inertia K = effective dynamic imbalance, nondimensional L = Lagrange function n s = inertial nutation frequency p,q,r,s = dimensionless parameters T = external torque applied to the system Tj = jet torque T M = internal motor torque t = time, nondimensional time a,/3 = dimensionless parameters defined in Eq. (9) 0 = cone angle, angle between axis 3 and H \ = Lagrange multiplier /i = nondimensional dynamic asymmetry a/ = /,//,,/= 1,3 CO/ = normalized time = normalized time at t = 0 = phase angle between axes 1 of the system frame and the nonresonant body = transverse angular velocity vector = initial spin angular velocity of rotor and platform = transverse angular velocity, component /,. i = 1,2 = rotor transverse angular velocity, spin component = platform transverse angular velocity, spin component

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confidence: 99%