The influence of inertia, eccentricity and atmospheric forces on the attitude dynamics of gravity oriented, non-spinning, axi-symmetric satellites, executing general librational motion is investigated using analytical, numerical and analog techniques. The problem is studied in the increasing order of complexity. For the case of a circular orbit, the autonomous, conservative system represented by constant Hamiltonian yields zero-velocity curves and motion envelopes which identify regions of instability from conditional and guaranteed stable motion. The non-linear, coupled equations of motion are solved using approximate analytical techniques: Butenin’s variation of parameter method and invariant integral approach. A comparison with the numerical response, establishes their suitability in studies involving motion in the small. The invariant integral method maintains reasonable accuracy even for larger, predominantly planar, disturbances. However, for a general motion in the large, the analytical solutions provide only qualitative information and one is forced to resort to numerical, analogic or hybrid procedures. The analysis suggests strong dependence of system response on the in-plane disturbances and satellite inertia. The librational and orbital frequencies are of the same order of magnitude. It also shows that the stable solution, when represented in a three dimensional phase space may lead to 'regular', 'ergodic' or 'island' type regions. The limiting integral manifolds, given here for a few representative values of Hamiltonian, provide all possible combinations of initial conditions, which a satellite can withstand without tumbling. The results, for a range of satellite inertia, are condensed in the form of design plots, indicating allowable disturbances for stable motion. In general, the slender satellites exhibit better stability characteristics. The presence of aerodynamic torque destroys the symmetry properties of the integral manifolds. The stability of the equilibrium configuration, which now deviates from the local vertical, is established through Routh's as well as Liapunov's criteria. As the system is still autonomous and conservative, the Hamiltonian remains constant leading to the bounds of libration. Numerical analysis of the system response indicates increased sensitivity to planar disturbances. The distortion and contraction of the regular, ergodic and island type stability regions show the adverse effects of aerodynamic torque. The design plots suggest that the shorter satellites, normally not preferred from gravity-gradient considerations, could exhibit better stability characteristics in the presence of large aerodynamic torque. An alternate, economical approach to the dynamical analysis of the satellites is attempted using an analog computer. A comparison with the digital data establishes the suitability of the method for design purposes and real time simulation. As the regular surface represents the only usable stability region from design considerations, a detailed study to establish the bound between regular and ergodic type stability was undertaken. The periodic solutions, obtained numerically using variable secant iteration show their spinal character with the body of stability region built around them. Of particular significance is the fundamental periodic solution (two planar oscillations in one out-of- plane cycle) associated with the regular region, suitable for practical operation of a satellite. The remaining periodic solutions represent degeneration of the island-like areas surrounding the mainland. The results lead to a set of fundamental periodic solutions over a wide range of system parameters. Floquet's variational analysis is used to establish the critical disturbance [formula omitted], beyond which no stable motion can be expected. The periodic solutions together with the regular stability region are presented here as functions of Hamiltonian, satellite inertia and aerodynamic torque. The case study of GEOS-A satellite is also included. In elliptic orbit, the Butenin's analysis of coupled forced systems is found to give an approximate solution of good accuracy. However for this non-autonomous situation, where Hamiltonian is no longer a constant of the motion, the concept of integral manifold breaks down. Fortunately, the design plots can still be generated by direct utilization of the response characteristics. In general the stability region diminishes with increasing eccentricity and disappears completely for e > 0.35. The presence of atmosphere adds to the complex behaviour of this non-autonomous system, where even the equilibrium configuration now becomes periodic in character. The stability regions are further reduced with instabilities normally initiating in the planar degree of freedom. Finally, a possibility of using the atmospheric forces in attitude control is explored. The use of a set of horizontal flaps in conjunction with a semi-passive, velocity-sensitive controller appears to be promising. With a suitable choice of system parameters even a large disturbance can be damped in approximately two orbits. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A general formulation is presented for the librational dynamics of satellites having an arbitrary number, type, and orientation of flexible appendages, each capable of deploying independently. In particular, the case of beam-type appendages deploying from a satellite in an arbitrary orbit is considered. The governing nonlinear, nonautonomous, coupled system equations are not amenable to any closed form solution, hence are integrated numerically using a digital computer. Effect of important system parameters is assessed through illustrative configurations representing a large class of gravity gradient and spinning spacecraft. Rather than accumulation of a large amount of data, the emphasis is on evolution of a generalized and organized methodology for coping with such complex dynamical systems. The analysis examines the degree of interaction between flexibility, deployment, and attitude motion through systematic variation of system parameters. A study of appendage vibration characteristics suggest that an orbiting beam cannot be treated simply as a rotating beam because of the presence of the gravitational field. Rate of rotation plays a dominant role in stiffening the beam as evidenced by the noticeable straightening of the eigen-functions for even relatively low spin rates (2 rpm). Results also show that the deployment-related Coriolis force can play a major role in causing large in-plane deformations. This implies that, in some cases, deployment should be carried out in stages so as to limitthe time available to build up large amplitude oscillations. Investigation of librational response shows that the coupled character of the motion can significantly affect system dynamics, hence caution should be exercised in utilizing results based on simplified planar analyses. Depending on orbital parameters and physical properties of booms, there are critical values of appendage length and deployment rate for which the satellite can tumble over. On the other hand, in general, appendage offset and shifting center of mass were found to have insignificant effect on response for the cases considered. This may permit considerable simplification of the complex hybrid equations with associated saving in computational time and effort. Also, the small amplitude oscillations evident both with the gravity gradient and spin-stabilized configurations tends to substantiate the adoption of a linear vibration analysis. The simulation of such diverse classes of satellites with relative ease demonstrates the versatility of the formulation. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The thesis aims at studying the dynamics of single and multibody systems with a variety of spacecraft oriented applications including configuration control for an instrumentation payload deployed from a spacecraft, the Solar Satellite Power Station (SSPS), a Space Shuttle supported tethered payload, etc. The problem is approached in an increasing order of complexity. In the beginning librational dynamics and force distribution for an axisymmetric, gravity oriented, rigid configuration are considered. The governing nonlinear, nonautonomous and coupled equations of motion are analyzed using Butenin's variation of parameter approach in conjunction with the Poincare-type expansion method, and the validity of the solutions established through numerical integration. The closed-form character of the solutions proved useful in identifying periodic solutions and resonance characteristics of the system. Furthermore, they provided considerable insight into the system behaviour over a range of the orbital eccentricity, inertia parameter and initial disturbances. Application of the analysis is demonstrated through the Gravity Gradient Test Satellite (GGTS). Next, general equations of librational motion, force and moment are derived for an arbitrarily-shaped, rigid spacecraft and approximate closed-form solutions obtained for spinning and gravity oriented systems using the Poincare-type analysis. The approach yields useful information concerning response to external disturbances as affected by the system parameters. The method is applied to several configurations: Explorer XX, an instrument package deployed from the Space Shuttle and the SSPS. Finally, a general dynamical formulation for a triaxial multibody system, in a circular orbit, with an elastic interconnecting link in the form of a tether or a beam is developed. The highly complicated coupled, nonlinear, nonautonomous equations of motion are linearized and their exact solution presented. Also expressions for forces and moments required to orient an object in space are obtained. This analytical procedure is applied to several configurations of practical interest. Throughout, the emphasis is on evolving a general formulation of the problem and its acceptable solution. Numerical results are presented only to appreciate significant response characteristics of the system. The general character of the analysis should prove useful in studying the dynamics of a wide range of existing and future spacecraft. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This investigation is concerned with the dynamic characteristics and stability of a spinning rigid body with a number of flexible parts. The system is hybrid in the sense that it is described by coordinates depending on time alone and coordinates depending on spatial position and time. The space-dependent coordinates are discretized by the assumed-modes method based on the Rayleigh-Ritz approach. The matrix form of the linearized equations of motion, which is of gyroscopic type, can be reduced to a general matrix multiplied by the state vector. The constrained system Hamiltonian is employed as a Liapunov function for stability analysis. It is shown that for stable nontrivial equilibrium the mass matrix and the stiffness matrix must be positive definite. In this case, the general matrix multiplied the state vector becomes skew-symmetric and its eigenvalues are complex conjugate pure imaginary. The method has been applied to the simplified model of the European Space Agency's GEOS spacecraft to obtain explicit forms of the equations of motion and stability criteria in terms of system parameters. It is found that the motion about the equilibrium is stable but the fundamental frequency is lower than the spin rate. As a by-product, it is shown that neglecting the motion of the mass center is immaterial as far as the stability is concerned, except in the case in which the points of attachment of the flexible parts are off-set along the spin axis relative to the mass center of the spacecraft. In the latter case, the effect of the motion of the mass center must be examined carefully. / Ph. D.

No description available.

The equations of motion for a satellite with a rigid central body and a pair of appendages deforming due to thermal effects of the solar radiation are derived. The dynamics of the system is studied in two stages: (i) librational dynamics of the central body with quasi-steady thermally flexed appendages; (ii) coupled librational/vibrational dynamics of the spacecraft. Response of the system is investigated numerically over a range of system parameters and effect of the thermal deformations assessed. The study indicates that for a circular orbit, the flexible system can become unstable under critical combinations of system parameters and initial conditions although the corresponding rigid system continues to be stable. However, in eccentric orbits, depending on the initial conditions, thermally flexed appendages can stabilize or destabliIize the system. Attempt is also made to obtain an approximate closed-form (analytical) solution of the problem to quickly assess trends and gain better physical appreciation of response characteristics during the preliminary design. Comparisons with numerical results show approximate analysis to be of an acceptable accuracy for the intended objective. The closed-form solution can be used with a measure of confidence thus promising a substantial saving in time, effort, and computational cost. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

No description available.

Master of Science

This thesis presents the computer model FORWP that is capable of predicting attenuation and cross polarization at 10-30 GHz from dual-polarization radar data with a high degree of accuracy. FORWP uses a rigorous backscattering computer model BSCAT to infer rain drop size distribution along the slant path from radar measured reflectivity and differential reflectivity data collected along the path. Then, two semi-empirical models are developed which predict attenuation from radar measured reflectivity and differential reflectivity. These two semi-empirical models are used to evaluate FORWP. Finally, attenuation predictions of FORWP are compared to the two semi-empirical prediction models and measured link attenuation at 11.4 GHz for a rain event in southwest Virginia. / M.S.

This paper presents a Lagrangian formulation for studying the dynamics and control of the proposed Space Station based Mobile Servicing System (MSS) for a particular case of in plane libration and maneuvers. The simplified case is purposely considered to help focus on the effects of structural and joint flexibility parameters of the MSS on the complex interactions between the station and manipulator dynamics during slewing and translational maneuvers. The response results suggest that under critical combinations of parameters, the system can become unstable. During maneuvers, the deflection of the MSS can become excessive, leading to positioning error of the payload. At the same time the libration error can also be significant. A linear quadratic regulator is designed to control the deflection of the manipulator and maintain the station at its operating configuration. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate