Gyroscopic control of a rigid body constrained to rotate about a fixed axis
Gyroscopic control of spin rate or orientation of rigid bodies constrained to rotate about fixed axis
Headrick, M. R.↗
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Results for “RIGID BODY”
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Gravitational waves from rotating and precessing rigid bodies. II - General solutions and computationally useful formulas
A rigid, freely precessing Newtonian body emits gravitational radiation. In this paper 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 for computing the exact gravitational power radiated and waveforms produced by arbitrary rigid-body freely precessing source are given. Also presented are the dominant terms 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.
Zimmermann, M.↗
Torques on a nearly rigid body in a relativistic gravitational field
The effect of post-Newtonian potentials on the rotation of a nearly rigid body is shown to consist of a precession and a torque. The frequency of the precession can be exactly represented by means of suitable differential operators. The relativistic torques in the quadrupole approximation depend on the instantaneous orientation of the principal axes of one body with respect to the position like the classical torque and velocity of the other. For a relatively low mass body, such as a gyroscope, these velocity-dependent torques have no observable consequences.
Caporali, A.↗
Recursive dynamics of topological trees of rigid bodies via Kalman filtering and Bryson-Frazier smoothing
The inverse and forward dynamics problems for a set of rigid bodies connected by hinges to form a topological tree are solved by using recursive techniques from linear filtering and smoothing theory. An inward filtering sequence computes a set of constraint moments and forces. This is followed by an outward sequence to determine a corresponding set of angular and linear accelerations. An inward sequence begins at the tips of all of the terminal bodies of the tree and proceeds inwardly through all of the branches until it reaches the root. Similarly, an outward sequence begins at the root and propagates to all of the tree branches until it reaches the tips of the terminal bodies. The paper also provides an approach to evaluate recursively the composite multibody system inertia matrix and its inverse.
Rodriguez, G.↗
SYMBOD - A computer program for the automatic generation of symbolic equations of motion for systems of hinge-connected rigid bodies
A computer program is described that can automatically generate symbolic equations of motion for systems of hinge-connected rigid bodies with tree topologies. The dynamical formulation underlying the program is outlined, and examples are given to show how a symbolic language is used to code the formulation. The program is applied to generate the equations of motion for a four-body model of the Galileo spacecraft. The resulting equations are shown to be a factor of three faster in execution time than conventional numerical subroutines.
Macala, G. A.↗
Computer program for post-flight analysis of rigid body moments acting on a launch vehicle first stage
A FORTRAN coded computer program and method for evaluation of the rigid body disturbing moments for a launch vehicle first stage based on post-flight measurements is described. The technique is a straightforward deterministic approach. Residual moments are computed to satisfy the equations of motion. Residuals are expressed in terms of altered vehicle characteristics; the aerodynamic coefficients, thrust misalignment, and control effectiveness. This method was used on the Scout launch vehicle and uncovered several significant differences between flight data and wind tunnel data. The computer program is written in FORTRAN IV for a CDC CYBER 173 computer system.
Knauber, R. N.↗
Optimizing Simulated Trajectories Of Rigid Bodies
6D POST is general-purpose, six-degree-of-freedom computer program for optimization of simulated trajectories of rigid bodies. Direct extension of three-degree-of-freedom POST program. 6D POST program models trajectory of powered or unpowered vehicle operating at or near rotating planet. Used to solve variety of performance, guidance, and flight-control problems for atmospheric and orbital vehicles. Written in FORTRAN 77 and FORTRAN V.
Brauer, Garry L.↗
Estimation of motion parameters for a rigid body from its orthogonal projection
An estimate is presented of the motion parameters, namely, linear and angular velocities of a rigid body rotating and translating in three-dimensional-space. It is assumed that the velocities are constant and that only the orthogonal projection of the motion is observable. In particular, if (x, y, z) is the Cartesian coordinate, it is assumed that the projection of the motion on the x-y plane is observed and the information along the z coordinate is lost.
Ganguly, S.↗
Rigid-body motion extracted from total motion of a flexible body
Control system eliminates or reduces flexibility effects on the manual and automatic control of large flexible vehicles. It extracts rigid-body and flexible-body motion and adapts well when a flexible-body frequency coincides or nearly coincides with the control mode frequency.
Howard, J. C.↗
A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses
The equations of motion are derived, in vector-dyadic format, for a topological tree of coupled rigid bodies, point masses, and symmetrical momentum wheels. These equations were programmed, and form the basis for the general-purpose digital computer program N-BOD. A complete derivation of the equations of motion is included along with a description of the methods used for kinematics, constraint elimination, and for the inclusion of nongyroscope forces and torques acting external or internal to the system.
Frisch, H. P.↗
Hinge-connected rigid bodies
Package of subroutines solve minimum dimension sets of discrete coordinate equations of motion for arbitrary number of hinge-connected rigid bodies assembled in tree topology.
Fleischer, C. E.↗
Torques on a nearly rigid body in a relativistic gravitational field
The effect of post-Newtonian potentials on the rotation of a perfect fluid, nearly rigid body is shown to consist of a precession and a torque. The frequency of the precession can be exactly represented by means of suitable differential operators. The relativistic torques, in the quadrupole approximation, depend on the instantaneous orientation of the principal axes of one body with respect to the position - like the classical torque - and velocity of the other. For a relatively low-mass body, such as a gyroscope, these velocity-dependent torques have no observable consequences.
Caporali, A.↗
Generalized Predictive Control of Dynamic Systems with Rigid-Body Modes
Numerical simulations to assess the effectiveness of Generalized Predictive Control (GPC) for active control of dynamic systems having rigid-body modes are presented. GPC is a linear, time-invariant, multi-input/multi-output predictive control method that uses an ARX model to characterize the system and to design the controller. Although the method can accommodate both embedded (implicit) and explicit feedforward paths for incorporation of disturbance effects, only the case of embedded feedforward in which the disturbances are assumed to be unknown is considered here. Results from numerical simulations using mathematical models of both a free-free three-degree-of-freedom mass-spring-dashpot system and the XV-15 tiltrotor research aircraft are presented. In regulation mode operation, which calls for zero system response in the presence of disturbances, the simulations showed reductions of nearly 100%. In tracking mode operations, where the system is commanded to follow a specified path, the GPC controllers produced the desired responses, even in the presence of disturbances.
Kvaternik, Raymond G.↗
Identification of motion parameters of a rigid body from its orthogonal and perspective projections
An estimate is made of the motion parameters, namely, linear and angular velocities, of a rigid body rotating and translating in three-space. The authors assume that the velocities are constant and that the motion is not completely observable. They consider two separate cases of partial observations corresponding to the orthogonal and the perspective projections, respectively. If (x, y, z) is the Cartesian coordinate of the three-space, the authors assume in the first case that the projection of the motion on the x-y plane is observed. If (r, theta, phi) is the polar coordinates of the three-space, they assume in the second case that the parameter vector (theta, phi) is observed. The use of both of these cases to estimate the motion parameters is discussed.
Ganguly, S.↗
The problem of exact interior solutions for rotating rigid bodies in general relativity
The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.
Wahlquist, H. D.↗
Numerical integration in a rigid-body trajectory program
Comparison of fourth order Runge-Kutta numerical integration technique with two numerical integration formulas in mathematical models used for computing rigid body trajectories
Moore, J. E.↗
Secular solution for delta-V during spin rate change maneuvers of rigid body spacecraft
Analytic expressions have been found for Euler's Equations of Motion and for the Eulerian Angles for both symmetric and near symmetric rigid bodies under the influence of arbitrary constant body-fixed torques. These solutions have been used to solve for the secular terms in the translational delta-V equations in inertial space. This secular delta-V solution is of interest in application to spinning spacecraft in that it describes the average direction of the delta-V of the spacecraft during a spin-up maneuver. Numerical integration of the governing differential equations has verified that the secular delta-V solution is valid for large time and is accurate in many physical situations including spin-up maneuvers of the Galileo spacecraft.
Klumpe, E. W.↗
Solution of Euler's Equations of Motion and Eulerian Angles for near symmetric rigid bodies subject to constant moments
Analytic expressions are found for Euler's Equations of Motion and for the Eulerian Angles for both symmetric and near symmetric rigid bodies under the influence of arbitrary constant body-fixed torques. These solutions provide the body-fixed angular velocities and the attitude of the body, respectively, as functions of time. They are of special interest in applications to spinning spacecraft (such as the Galileo Spacecraft to be launched in 1984) because they include the effect of time-varying spin rate. Thus they can be applied to spin-up and spin-down maneuvers as well as to error analysis for thruster misalignments. The solutions are given for arbitrary initial conditions in terms of Fresnel, Sine and Cosine Integrals. Numerical integration of the governing differential equations has verified that the approximate analytic solutions are very accurate in many physical situations of interest.
Longuski, J. M.↗