Effect of gravity gradient torque on the motion of the spin axis of an asymmetric vehicle
Gravity gradient torque effect on spin axis motion of asymmetric vehicle in precessing circular orbit of oblate earth
CIRCULAR ORBIT↗
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Large angle method for space vehicle angular momentum desaturation using gravity gradient torques
Large angle method for space vehicle angular momentum desaturation using gravity gradient torque
Kennel, H. F.↗
Gravity gradient torque for an arbitrary potential function
To permit investigation of the relative effects of higher-order terms in the potential function and allow computation of the gravity gradient torques consistent with the gravitational acceleration for a given potential function, a simple formula is derived for computing the gravity gradient torque on a vehicle in terms of the eigenvalues and eigenvectors of the gravity gradient matrix and the inertia properties of the vehicle. The formulation is applicable to any potential function for which the gravity matrix can be computed for a given point in the potential field.
Glandorf, D. R.↗
The dynamics and optimal control of spinning spacecraft and movable telescoping appendages, part B: Effect of gravity-gradient torques on the dynamics of a spinning spacecraft with telescoping appendages
The effects of gravity gradient torques during boom deployment maneuvers of a spinning spacecraft are examined. Configurations where the booms extended only along the hub principal axes and where one or two booms are offset from the principal axes were considered. For the special case of symmetric deployment (principal axes booms) the stability boundaries are determined, and a stability chart is used to study the system behavior. Possible cases of instability during this type of maneuver are identified. In the second configuration an expression for gravity torque about the hub center of mass was developed. The nonlinear equations of motion are solved numerically, and the substantial influence of the gravity torque during asymmetric deployment maneuvers is indicated.
Bainum, P. M.↗
Effect of gravity-gradient torques on the dynamics of a spinning spacecraft with telescoping appendages
The effects of gravity-gradient torques during boom deployment maneuvers of a spinning spacecraft are examined with a combination of numerical and analytical methods. It is assumed that the spacecraft consists of a rigid central hub and movable rigid telescoping booms where the booms extend only along the hub principal axes. For the special case of symmetric deployment the stability boundaries are determined and a stability chart is used to study the system behavior. Possible cases of instability during this type of maneuver are identified.
Rajan, M.↗
A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque
Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.
Thompson, J. F.↗
Gravity gradient torque profiles over an orbit for arbitrary modular space station configurations in the Y-POP and inertial hold modes
For several proposed configurations of the modular space station, the gravity gradient torque distribution is examined for both Y-POP and inertial hold orbits. The necessary equations are derived to allow for solar panel gimbaling, and a procedure is established which will allow any desired space station configuration to be built up. Results indicated that solar panel gimbaling can be a significant factor in the torque distribution in Y-POP orbits. In addition, for the two configurations that were plotted, bias torque magnitudes varied widely in inertial hold modes.
Mcgill, D. J.↗
Fast gravity, gravity partials, normalized gravity, gravity gradient torque and magnetic field: Derivation, code and data
Derivation of first and second partials of the gravitational potential is given in both normalized and unnormalized form. Two different recursion formulas are considered. Derivation of a general gravity gradient torque algorithm which uses the second partial of the gravitational potential is given. Derivation of the geomagnetic field vector is given in a form that closely mimics the gravitational algorithm. Ada code for all algorithms that precomputes all possible data is given. Test cases comparing the new algorithms with previous data are given, as well as speed comparisons showing the relative efficiencies of the new algorithms.
Gottlieb, Robert G.↗
Effects of gravity-gradient torque on the rotational motion of a triaxial satellite in a precessing elliptic orbit.
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.
Cochran, J. E.↗
Angular momentum desaturation for Skylab using gravity gradient torques
An angular momentum desaturation method for momentum exchange devices of orbiting spacecraft is described. The specific application of the method is to the Skylab which contains three double-gimbaled control moment gyros for precise attitude control and maneuvering. It is assumed that the attitude reference is inertially fixed and that two of the vehicle principal moments of inertia are much larger than the third. Gravity gradient torques and resultant angular momentum accumulation are developed for small deviations from the reference. The assumed moment-of-inertia distribution allows desaturation about all axes with only two attitude angles each for the two axes with large moments of inertia. The necessary desaturation maneuvers can be decoupled for a special set of orbital coordinates. All maneuvers are made during the night portion of the orbit, and the percentage utilized for desaturation is selectable. Expressions for the attitude angle commands are developed assuming infinite vehicle rates. The effect of finite rates introduces an efficiency into the desaturation. Expressions for this efficiency are developed and means for compensation are treated. Arbitrary misalignments between geometric vehicle axes and principal moment-of-inertia axes are permissible. An angle bias about the sun line minimizes the angular momentum accumulation about the sun line projection into the orbital plane. Adaptive desaturation maneuver limiting consistent with the available maneuver momentum is included.
Kennel, H. F.↗
The effect of gravity-gradient torques on the three dimensional motion of a rotating space station-cable-counterweight system
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Bainum, P. M.↗
On the attitude motion of an orbiting rigid body under the influence of gravity gradient torque
An investigation is made of the rotational motion of a rigid body orbiting the earth, under the influence of the geogravity-gradient torque. The attitude dynamics are formulated as perturbations from a nominal case. The perturbed equations are solved asymptotically, by the multiple scales technique. The independent variable, time, is extended into a space of higher dimension by means of new scales, fast, slow, etc. Integration of the equations is carried out separately in the new variables. The rapid and slow aspects of the attitude dynamics are systematically separated, resulting in a more efficient computer implementation and enhanced physical insight. The theory is applied to predict the attitude dynamics of an asymmetric rigid body satellite. A comparison is made of the maximum errors as the step size increases as predicted by the multiple scales solution and direct numerical integration. An improvement in computational speed of an order of magnitude is demonstrated.
Tao, Y. C.↗
Measuring and Utilizing Gravity-Gradient Induced Torques on Future Gravity Recovery Missions
This research is a novel investigation into the use of newly-available relative angular acceleration measurements between a spacecraft utilized for gravity recovery missions and an internally located test mass. The gravity-gradient torque equation for zonal spherical harmonic order n is formulated for a known gravitational potential field, and through simulations it is proven that the Simplified-Gravitational Reference Sensor will be sensitive to the gravity-gradient induced torques acting on its test mass. The full conference paper will demonstrate how the presented gravity-gradient torque equation and the measured relative angular acceleration between the spacecraft and test mass will improve the accuracy of the gravity field models acquired by future gravity recovery missions by directly measuring the drag acting on the spacecraft with a single accelerometer.
gravity recovery↗
Computer simulation for attitude disturbance torques for the Tiros-series.
Description of the Tiros-M Magnetic Attitude Prediction Program (TMMGAP), a simulation program designed to assist in the rotational motion control of the Tiros-series spacecraft. The subsystems of the program include input, attitude simulation, executive, attitude control and output components, simulating solar radiation pressure torque, gravity gradient torque, residual magnetic moment torque, and magnetic attitude control torques. The program provides data for prelaunch studies for launch window selection and mission planning, facilitates spacecraft spin axis reorientation after launch, provides spin axis control recommendations to meet mission constraints, and assists in the interpretation of cloud cover data. The program is characterized as effective in controlling spin axis and in processing picture data.
Sugai, I.↗
Estimation of Gravitation Parameters of Saturnian Moons Using Cassini Attitude Control Flight Data
A major science objective of the Cassini mission is to study Saturnian satellites. The gravitational properties of each Saturnian moon is of interest not only to scientists but also to attitude control engineers. When the Cassini spacecraft flies close to a moon, a gravity gradient torque is exerted on the spacecraft due to the mass of the moon. The gravity gradient torque will alter the spin rates of the reaction wheels (RWA). The change of each reaction wheel's spin rate might lead to overspeed issues or operating the wheel bearings in an undesirable boundary lubrication condition. Hence, it is imperative to understand how the gravity gradient torque caused by a moon will affect the reaction wheels in order to protect the health of the hardware. The attitude control telemetry from low-altitude flybys of Saturn's moons can be used to estimate the gravitational parameter of the moon or the distance between the centers of mass of Cassini and the moon. Flight data from several low altitude flybys of three Saturnian moons, Dione, Rhea, and Enceladus, were used to estimate the gravitational parameters of these moons. Results are compared with values given in the literature.
angular momentum↗
The 100-meter radiometer spacecraft study
A rigid body analysis of a baseline Large Space System (LSS) which is to function as a radiometer is presented. The LSS is placed in circular orbit about the Earth at an altitude of 650 km, subjected to environmental and vehicle interaction forces and torques, without an active control system of any type on board. The environment forces and torques are gravity gradient, solar radiation, and aerodynamic. Normal operation is in nadir pointing along the Z-local vertical axis. Orbital velocity is assigned to the x-axis of the spacecraft. The analysis is then used to demonstrate the ability or lack of the gravity gradient torques to stabilize the LSS over one complete orbit.
Zimbelman, H. F.↗
Integrated Orbit, Attitude, and Structural Control Systems Design for Space Solar Power Satellites
The major objective of this study is to develop an integrated orbit, attitude, and structural control systems architecture for very large Space Solar Power Satellites (SSPS) in geosynchronous orbit. This study focuses on the 1.2-GW Abacus SSPS concept characterized by a 3.2 x 3.2 km solar-array platform, a 500-m diameter microwave beam transmitting antenna, and a 500 x 700 m earth-tracking reflector. For this baseline Abacus SSPS configuration, we derive and analyze a complete set of mathematical models, including external disturbances such as solar radiation pressure, microwave radiation, gravity-gradient torque, and other orbit perturbation effects. The proposed control systems architecture utilizes a minimum of 500 1-N electric thrusters to counter, simultaneously, the cyclic pitch gravity-gradient torque, the secular roll torque caused by an offset of the center-of-mass and center-of-pressure, the cyclic roll/yaw microwave radiation torque, and the solar radiation pressure force whose average value is about 60 N.
Wie, Bong↗
Integrated Orbit, Attitude, and Structural Control System Design for Space Solar Power Satellites
The major objective of this study is to develop an integrated orbit, attitude, and structural control system architecture for very large Space Solar Power Satellites (SSPS) in geosynchronous orbit. This study focuses on the 1.2-GW Abacus SSPS concept characterized by a 3.2 x 3.2 km solar-array platform, a 500-m diameter microwave beam transmitting antenna, and a 500 700 m earth-tracking reflector. For this baseline Abacus SSPS configuration, we derive and analyze a complete set of mathematical models, including external disturbances such as solar radiation pressure, microwave radiation, gravity-gradient torque, and other orbit perturbation effects. The proposed control system architecture utilizes a minimum of 500 1-N electric thrusters to counter, simultaneously, the cyclic pitch gravity-gradient torque, the secular roll torque caused by an o.set of the center-of-mass and center-of-pressure, the cyclic roll/yaw microwave radiation torque, and the solar radiation pressure force whose average value is about 60 N.
Wie, Bong↗