The three dimensional motion and stability of a rotating space station-cable - Counterweight configuration

The three dimensional equations of motion for a cable connected space station - counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the in-plane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria

Nutational stability of a dual-spin satellite under the influence of applied reaction torques

It is assumed that since the solar paddle attachments to the hub of the spacecraft are not rigidly locked, the effect of the solar panels can be replaced by a constant reaction torque acting on the hub of the spacecraft. This could result in the satellite having an equilibrium motion about an axis displaced from the nominal axis of symmetry. The variational equations of motion are developed about such an equilibrium position using the SAS-A spacecraft as a model. Energy dissipation on the rotor as well as the main body is included. This nonautonomous set of differential equations are linearized and transformed to an autonomous set using the Liapunov reducibility theorem. The stability of the kinematically similar system is examined numerically using representative SAS-A parameters for the case when either pair of solar panels is assumed to be loosely attached. Stability is verified for small system nutation angles (0.1 degree)

The dynamics and optimal control of spinning spacecraft and movable telescoping appendages, part A

The problem of optimal control with a minimum time criterion as applied to a single boom system for achieving two axis control is discussed. The special case where the initial conditions are such that the system can be driven to the equilibrium state with only a single switching maneuver in the bang-bang optimal sequence is analyzed. The system responses are presented. Application of the linear regulator problem for the optimal control of the telescoping system is extended to consider the effects of measurement and plant noises. The noise uncertainties are included with an application of the estimator - Kalman filter problem. Different schemes for measuring the components of the angular velocity are considered. Analytical results are obtained for special cases, and numerical results are presented for the general case

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

On the accuracy of modelling the dynamics of large space structures

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column

Spacecraft detumbling using movable telescoping appendages

The dynamics of detumbling a randomly spinning spacecraft using externally mounted, movable telescoping appendages were studied both analytically and numerically. Two types of telescoping appendages are considered: where an end mass is mounted at the end of an (assumed) massless boom; and where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. From an application of Liapunov's second method, boom extension maneuvers were determined to approach either of two desired final states: close to a zero inertial angular velocity state, and a final spin rate about only one of the principal axes. Recovery dynamics are evaluated analytically for the case of symmetrical deployment. Numerical examination of other asymmetrical cases verifies the practicality of using movable appendages to recover a randomly tumbling spacecraft

The dynamics and control of large flexible space structures. Part A: Discrete model and modal control

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems were investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit was analyzed. First order effects of gravity gradient were included. A mathematical model which describes the system rotations and deflections within the orbital plane was developed by treating the beam as a number of discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of the system are simulated and, in addition, the effects of the control devices were considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, was examined. The effect of varying the number of modes in the model as well as the number and location of the control devices were also considered

The dynamics of spin stabilized spacecraft with movable appendages, part 1

The motion and stability of spin stabilized spacecraft with movable external appendages are treated both analytically and numerically. The two basic types of appendages considered are: (1) a telescoping type of varying length and (2) a hinged type of fixed length whose orientation with respect to the main part of the spacecraft can vary. Two classes of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. For the telescoping system Eulerian equations of motion are developed. During all deployment sequences it is assumed that the transverse component of angular momentum is much smaller than the component along the major spin axis. Closed form analytical solutions for the time response of the transverse components of angular velocities are obtained when the spacecraft hub has a nearly spherical mass distribution

The dynamics and optimal control of spinning spacecraft with movable telescoping appendages. Part C: Effect of flexibility during boom deployment

The dynamics of a spinning symmetrical spacecraft system during the deployment (or retraction) of flexible boom-type appendages were investigated. The effect of flexibility during boom deployment is treated by modelling the deployable members as compound spherical pendula of varying length (according to a control law). The orientation of the flexible booms with respect to the hub, is described by a sequence of two Euler angles. The boom members contain a flexural stiffness which can be related to an assumed effective restoring linear spring constant, and structural damping which effects the entire system. Linearized equations of motion for this system, when the boom length is constant, involve periodic coefficients with the frequency of the hub spin. A bounded transformation is found which converts this system into a kinematically equivalent one involving only constant coefficients

The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures

The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out