A Two-Gyro, Gravity-Gradient Satellite Attitude Control System

Lewis, Jeffrey A.; Zajac, E. E.

doi:10.1002/j.1538-7305.1964.tb01025.x

Cited by 15 publications

(10 citation statements)

References 14 publications

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“…We consider the case in which the satellite is moving in a slightly elliptical orbit, and suppose that the pitch axis of the satellite remains perpendicular to the orbit plane. The occurrence of such pitching motions is indicated by the results of Lewis and Zajac, 1 and is consistent with their model, which is the one considered here. If the pitch axis of the satellite is not perpendicular to the orbit plane, then the pitching motion is coupled to other motions.…”

Section: Introductionsupporting

confidence: 83%

“…1. The equations of motion then are transformed by taking the polar angle of the satellite center of mass as the independent variable, rather than the time.…”

Section: Introductionmentioning

confidence: 99%

“…1 The attitude control system involves two single-degree-of-freedom gyroscopes in a socalled roll-vee configuration, and is depicted schematically in Fig. 1, relative to the principal axes of the satellite.…”

Section: Introductionmentioning

confidence: 99%

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Stationary resonant pitching motions of a controlled satellite.

Morrison¹

1969

AIAA Journal

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A controlled satellite moving in a slightly elliptical orbit, with one axis of the satellite perpendicular to the orbit plane, is considered. The control system involves two single-degreeof-freedom gyroscopes in a so-called roll-vee configuration. The stationary, resonant, nonlinear oscillatory and rotary states, and their stability, are determined, under the assumption that the eccentricity of the orbit and the gyro damping rate are sufficiently small. Both forward and retrograde rotations are considered. It is found that the stable stationary states are strictly stable, rather than neutrally so as in the case of an uncontrolled satellite. The gimbal angle is zero, in the lowest-order approximation, for the stationary oscillatory states. For the forward stationary rotary states, the gyro gimbals are partially collapsed towards the pitch axis. For the retrograde stationary rotary states, the gyro gimbals are spread away from the pitch axis, and unless the nominal roll-vee angle is less than a certain quantity, the gyro gimbals will be against the yaw stops, which is not permitted by the analysis.

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Section: Introductionsupporting

confidence: 83%

“…1. The equations of motion then are transformed by taking the polar angle of the satellite center of mass as the independent variable, rather than the time.…”

Section: Introductionmentioning

confidence: 99%

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Stationary resonant pitching motions of a controlled satellite.

Morrison¹

1969

AIAA Journal

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“…Such mechanical systems are delivered to orbit compactly packaged and then are deployed there. There is literature on the deployment of elastic elements from a fixed base and from a spinning spacecraft [9,[11][12][13]23], including the deployment of a gravity-gradient boom [15,19]. In these studies, the maximum bending moments, deflections of booms, and optimal deployment time were assessed using various simplifying assumptions.…”

mentioning

confidence: 99%

Dynamics of an Unstabilized Spacecraft During the Deployment of an Elastic Pantograph Structure

Zakrzhevskii

Khoroshilov

2014

Int Appl Mech

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An unstabilized spacecraft with a pantograph structure deployed in orbit to carry solar batteries is the subject of study. The objective of the study is to construct a mathematical model of this system taking into account the elastic properties of elements of the pantograph in longitudinal and transverse directions. This model is based on the Lagrangian formalism as applied to a mechanical system with rheonomic constraints. The expressions for the coefficients of the equations of motions are obtained using Mathematica 5 © . A Fortran application software package is used for numerical simulation of dynamic processes. This package can be adapted, if necessary, to study other structures. The behavior of the spacecraft during the deployment of the pantograph is numerically analyzed using different values of spacecraft parameters and the parameters of the deployment process in the gravity field.Introduction. The dynamics of reconfigurable systems is one of the promising and important research areas in mechanics [9,[11][12][13]23]. Modern spacecraft incorporate various components that are deployed in orbit (solar batteries (SB), gravity-gradient booms, antennas, etc.). Such mechanical systems are delivered to orbit compactly packaged and then are deployed there. There is literature on the deployment of elastic elements from a fixed base and from a spinning spacecraft [9,[11][12][13]23], including the deployment of a gravity-gradient boom [15,19]. In these studies, the maximum bending moments, deflections of booms, and optimal deployment time were assessed using various simplifying assumptions. Cherchas [14] studied the dynamics of spin-stabilized satellites during the extension of long flexible booms. He has determined the maximum nutation and precession angles after the deployment of the boom and its maximum bending moments and deflections, derived the equations of motion using Lagrange's equations, and discretized the elastic degrees of freedom by a modal analysis. In [20,21,24], the dynamics of deployable elastic elements is also described in terms a modal analysis with time-dependent natural modes.Banerjee and Kane [7] present a new method for simulating the motion of a beam that is being extruded from, or retracted into a rotating rigid body. In essence, the method consists of modeling the beam as a series of elastically connected rigid links and then working with equations of motion linearized in the modal coordinates for the links outside the rigid body. In [6,8], the analysis was extended to large deflections and used an order-n formulation for a variable number of bodies. The modeling has revealed that the tip deflections are very sensitive to the extrusion/retraction rate, the retraction process is less stable than the extrusion process, and the behavior of the beam is strongly dependent on the angular rate of the body.The deployment of such elements is a substantial perturbation to the motion of the spacecraft around its center of mass. It is impossible to model such perturbations within the framework of the...

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“…A description of an attitude control system for a gravitationally oriented earth-pointing satellite has been given by J. A. Lewis and E. E. Zajac [1]. The attitude control system involves two single-degree-of-freedom gyroscopes in a so-called roll-vee configuration.…”

mentioning

confidence: 99%

On the damping of a satellite motion

Morrison¹

1964

Quart. Appl. Math.

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The motion in a circular orbit of a gravitationally oriented satellite, whose angular motions about the local vertical are damped by a roll-vee, gyrostabilizer system, is considered, wherein the pitch axis of the satellite remains perpendicular to the orbital plane. It is shown that no matter how large the initial local angular velocity of the satellite is, this velocity reaches any given smaller value in a finite time. It is also shown how it is possible to obtain a bound on this damping time.1. Introduction and summary. A description of an attitude control system for a gravitationally oriented earth-pointing satellite has been given by J. A. Lewis and E. E. Zajac [1]. The attitude control system involves two single-degree-of-freedom gyroscopes in a so-called roll-vee configuration. In the desired motion, the satellite describes a circular orbit and has one axis continuously aligned along the local vertical. If at any given instant the satellite is not aligned along the local vertical with the proper angular velocity of one rotation per orbit, the gyroscopes precess about their output axes and undergo viscous damping, so that at least for small initial disturbances the satellite finally settles out in one of two possible earth-pointing positions.It is of importance to be sure that the gyroscopes will damp out the angular librations of the satellite for arbitrary initial conditions, including the case of tumbling. Heretofore the only available evidence has consisted of plausibility arguments and a limited number of numerical solutions of the differential equations of motion, for moderately large initial angular rates. The present paper contains a rigorous proof that for a limited class of motions (that is, pure pitching motions), satellite damping occurs for arbitrarily large initial angular rates.In the motions considered, the satellite revolves in a circular orbit and rotates so that its so-called "pitch" axis remains perpendicular to the orbital plane. The differential equations describing this motion take the form ft" + a2 sin 2/3 + p 0, (1.3)where /3 is the angle of rotation of the satellite measured with respect to the local vertical, and the dot superscript denotes differentiation with respect to time. The gyros are symmetrically situated with respect to the pitch axis and hence only one gimbal angle

0; m > 0; p > 0; q > 0; 0 < a < |* (1.4) *Received August 15, 1963.

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A Two-Gyro, Gravity-Gradient Satellite Attitude Control System

Cited by 15 publications

References 14 publications

Stationary resonant pitching motions of a controlled satellite.

Stationary resonant pitching motions of a controlled satellite.

Dynamics of an Unstabilized Spacecraft During the Deployment of an Elastic Pantograph Structure

On the damping of a satellite motion

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