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Space shuttle boost vehicle with various degrees of aerodynamic stability, discussing control laws effects on rigid body bending moment tradeoff
A very simple, yet accurate, heuristic solution for the spiral path of the angular momentum vector during spin-up and spin-down maneuvers of rigid body spacecraft is presented. A two-burn scheme is proposed consisting of a burn, a coast, and a second burn of the spin thruster. The appropriate burn times are found by a transcendental equation similar to Kepler's equation. Numerical results verify the accuracy of the burn, coast, and burn times given by closed form expressions. The scheme can also be applied to the problem of axial thrusting during constant spin.
A brief description is presented of a canonical set of equations which governs the behavior of an n-body spacecraft. General results are given for the case in which the spacecraft is modeled in terms of n rigid bodies connected by dissipative elastic joints. The final equations are free from constraint torques and involve only r variables (r is the number of degrees of freedom of the system). An advantage which accompanies the elimination of the constraint torques is a decrease in the computer run time (especially when n is large).
Several computer subroutines are designed to provide the solution to minimum-dimension sets of discrete-coordinate equations of motion for systems consisting of an arbitrary number of hinge-connected rigid bodies assembled in a tree topology. In particular, these routines may be applied to: (1) the case of completely unrestricted hinge rotations, (2) the totally linearized case (all system rotations are small), and (3) the mixed, or partially linearized, case. The use of the programs in each case is demonstrated using a five-body spacecraft and attitude control system configuration. The ability of the subroutines to accommodate prescribed motions of system bodies is also demonstrated. Complete listings and user instructions are included for these routines (written in FORTRAN V) which are intended as multi- and general-purpose tools in the simulation of spacecraft and other complex electromechanical systems.
In this paper, we present a tensorial derivation of the equations of motion of a formation consisting of N spacecraft each modeled as a rigid body.
Some methods of approaching a solution to the Hamilton-Jacobi equation are outlined and examples are given to illustrate particular methods. These methods may be used for cases where the Hamilton-Jacobi equation is not separable and have been particularly useful in solving the rigid body motion of an earth satellite subjected to gravity torques. These general applications may also have usefulness in studying the motion of satellites with aerodynamic torque and in studying space vehicle motion where thrusting is involved.
The classical mechanics results for free precession which are needed in order to calculate the weak field, slow-motion, quadrupole-moment gravitational waves are reviewed. Within that formalism, algorithms are given for computing the exact gravitational power radiated and waveforms produced by arbitrary rigid-body freely-precessing sources. The dominant terms are presented in series expansions of the waveforms for the case of an almost spherical object precessing with a small wobble angle. These series expansions, which retain the precise frequency dependence of the waves, may be useful for gravitational astronomers when freely-precessing sources begin to be observed.
Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at the early stages of preliminary design and development. For these early analyses an approximate, but reasonably accurate, set of equations of motion for elastic airplanes is needed. Such a formulation is developed for the lateral dynamics of elastic airplanes. It makes use of rigid-body aerodynamic stability derivatives and the antisymmetric elastic mode shapes and frequencies in formulating the forces and moments due to elastic motion. Verification of accuracy was made by comparison with B-1 airplane dynamics obtained by other methods. Frequencies and damping ratios of the coupled modes agree acceptably well with four antisymmetric elastic modes included.
Variational equations were applied to the case of a rapidly spinning triaxial body moving in an elliptic orbit, in which the orbital plane is regressing at a constant rate. The explicit differential equations obtained in this application were integrated by the method of averaging to develop secular analytical expressions, which, to first-order in a small parameter, describe the complete space motions of the rigid body under the influence of nonresonant gravity-gradient perturbations. The effects of aerodynamic torque on the rotational motion of an orbiting satellite are studied, as another example of the application of the variational equations derived and the method of averaging.
The Large UV/Optical/IR Surveyor (LUVOIR) is a conceptual space observatory under development by NASA Goddard Space Flight Center for the Astronomy and Astrophysics Decadal Survey. As with similar space telescopes, e.g., James Webb, this spacecraft will have ultra-stringent pointing stability requirements, i.e., on the order of miliarcseconds. Thus, the design of the LUVOIR attitude control system (ACS) may benefit from a model-based approach. In this document, we present an approximate model of the LUVOIR composed of two 3D rigid bodies connected by a 1-DOF rotary joint. From this model, we derive the nonlinear equations of motion, following the approach of Eric T. Stoneking [1], and linearize them about an arbitrary reference orientation. Using the subsequent state space representation, it is straightforward to compute a set of control gains (e.g., via the ”lqr” or ”place” commands in MATLAB). We conclude this memo with a comparison of our LQR approach with the existing PID slew controller designed by a former NASA intern.
Averaging technique applied to variational equations describing rotational motions of rigid triaxial body in elliptical orbit
Celestial mechanics perturbation methods applied to problem of describing motion of rigid artificial earth satellite about its center of mass
In the design/analysis process of a payload structural system, the accelerations at the payload/launch vehicle interface obtained from a system analysis using a rigid payload are often used as the input forcing function to the elastic payload to obtain structural design loads. Such an analysis is at best an approximation since the elastic coupling effects are neglected. This paper develops a method wherein the launch vehicle/rigid payload interface accelerations are modified to account for the payload elasticity. The advantage of the proposed method, which is exact to the extent that the physical system can be described by a truncated set of generalized coordinates, is that the complete design/analysis process can be performed within the organization responsible for the payload design. The method requires the updating of the system normal modes to account for payload changes, but does not require a complete transient solution using the composite system model. An application to a real complex structure, the Viking Spacecraft System, is given.
A discrete momentum-conserving explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid-point implicit formula for integrating the Euler parameters and a second-order discrete momentum-conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.
Background Stereo-DIC is a widely used optical measurement technique that provides a dense full-field 3D measurement of the shape, displacement, and strain of a solid sample. When compared with 2D-DIC, Stereo-DIC provides greater flexibility and expands its use beyond flat, planar specimens. Furthermore, the widespread availability of commercial systems has led to the adoption of the technique throughout industry, academia, and government research labs. Objective Even though some research has been done to understand the effects of different experimental and stereo-DIC parameters, no reference is available to benchmark and compare the performance of current stereo-DIC algorithms to each other. Methods This paper provides the description and analysis of a carefully controlled 3D experiment and associated images used to compare the results from five subset based DIC software packages. Both the images and analysis codes used in this paper to compare the results are described here and are available for download and use for continued research. Results We show that over a very large range of motion, the 3D errors are very small, less than 80μm over a travel of ±20 mm out-of-plane and ±20 mm in-plane. While all codes performed similarly, there are important differences noted in the paper. Conclusion The image sets and results comparison software are hosted by the International DIC Society (www.iDICs.org) and are freely available for download and analysis for comparison with results in this paper. Furthermore, it is hoped that this set of images can be used for future research in improving stereo-DIC by future authors.
Minimum fuel control of spacecraft in orbit using extended method of steepest descent
Liapunov stability derived from kinetic energy and squared angular momentum
Dynamic formalism and computer program for multiple space vehicle attitude and control simulations