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  • 1
    Electronic Resource
    Electronic Resource
    The influence of satellite flexibility on orbital motion (1978)
    Springer
    Celestial mechanics and dynamical astronomy 17 (1978), S. 145-165 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The orbital perturbations induced by the librational motion and flexural oscillations are studied for satellites having large flexible appendages. Using a Lagrangian procedure, the equations for coupled motion are derived for a satellite having an arbitrary number of appendages in the nominal orbital plane and two flexible members normal to it. The formulation enables one to study the influence of flexibility on both the orbital and attitude motions. The orbital coordinates are expanded as perturbation series in ε=(l/a 0)2,l anda 0 being a characteristic length of the satellite and unperturbed semi-major axis of the orbit, respectively. The first order perturbation equations are solved in terms of elastic deformations and librational angles using the WKBJ method in conjunction with the variation of parameter technique. Existence of secular perturbations is noted for certain librational flexural motions. Three specific examples, Alouette II, Radio Astronomy Explorer and Tethered Orbiting Interferometer, are considered subsequently and their possible secular drifts estimated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01371327
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  • 2
    Electronic Resource
    Electronic Resource
    Long-term evaluation of three-dimensional heliocentric solar sail trajectories with arbitrary fixed sail setting (1979)
    Springer
    Celestial mechanics and dynamical astronomy 19 (1979), S. 113-138 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The solar radiation effects upon the orbital behaviour of an arbitrarily shaped spacecraft (or a solar sail in particular) in a general fixed orientation with respect to the local coordinate frame are investigated. Through introduction of a quasi-angle in the osculating plane, the motion of the orbital plane becomes uncoupled from the in-plane perturbations. Exact solutions in the form of conic sections and logarithmic spirals can readily be formulated for certain specific initial conditions. An effective out-of-plane spiral transfer trajectory is obtained by reversing the force component normal to the orbital plane at specified positions in the orbit. By choosing the appropriate control angles for the sail orientation, any point in space can be reached eventually. In the case of general initial conditions, the long-term orbital behaviour is assessed asymptotically by means of the two-variable expansion procedure. An implicit expression for the eccentricity is derived and explicit results are established by an iteration scheme. The other orbital elements can be expressed in terms of the eccentricity and their asymptotic series for near-circular initial orbits are also obtained. While equations for the higher-order contributions as well as the periodic parts of their solutions can be formulated readily, their secular terms are determined only for a circular initial orbit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01796085
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  • 3
    Electronic Resource
    Electronic Resource
    Asymptotic solutions in the many-body problem (1976)
    Springer
    Celestial mechanics and dynamical astronomy 14 (1976), S. 465-492 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A three-body problem is considered in which two masses, forming a close binary, orbit a comparatively distant mass. An asymptotic solution of this problem is presented, where the small parameter ε is related to the distance separating the binary and the remaining mass. Accepting certain model constraints, this solution is accurate within a constant errorO(ε11) and uniformly valid for time intervalsO(ε−3). Two specific examples are chosen to verify the literal solution: one relating to the Sun-Earth-Moon configuration of the solar system, the other to an idealized stellar system where the three masses are in the ratio 20:1:1. In both cases close agreement is found when the analytical solution is compared with an equivalent numerically-generated orbit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229058
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  • 4
    Electronic Resource
    Electronic Resource
    On the periodic solutions and resonance of spinning satellites in near-circular orbits (1975)
    Springer
    Celestial mechanics and dynamical astronomy 11 (1975), S. 195-212 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Attitude motion of spinning axisymmetric satellites in presence of gravity-gradient and solar radiation pressure torques is studied analytically. The approximate closed-form solution developed for the nonlinear, nonautonomous, coupled fourth-order system proves to be an excellent tool in locating periodic solutions of the system in both circular and noncircular orbits. The variational stability of the periodic motion is examined using the Floquet theory. The resonance analysis suggests the existence of critical combinations of system parameters leading to large amplitude oscillations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230545
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  • 5
    Electronic Resource
    Electronic Resource
    Asymptotic solutions in the many-body problem (1977)
    Springer
    Celestial mechanics and dynamical astronomy 15 (1977), S. 5-20 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A small particle moves in the vicinity of two masses, forming a close binary, in orbit about a distant mass. Unique, uniformly valid solutions of this four-body problem are found for motion near both equilateral triangle points of the binary system in terms of a small parameter ε, where the primaries move in accordance with a uniformly-valid three-body solution. Accuracy is maintained within a constant errorO(ε8), and the solutions are uniformly valid as ε tends to zero for time intervalsO(ε−3). Orbital position errors nearL 4 andL 5 of the Earth-Moon system are found to be less than 5% when numerically-generated periodic solutions are used as a standard of comparison.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229044
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  • 6
    Electronic Resource
    Electronic Resource
    On the periodic solutions of slowly spinning gravity gradient system (1972)
    Springer
    Celestial mechanics and dynamical astronomy 5 (1972), S. 126-143 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The paper emphasizes the importance of periodic solutions in the dynamic stability study of an axi-symmetric satellite in presence of gravity gradient torques. Initial conditions for periodic solutions are presented over a range of system parameters for motion in circular and elliptic orbits. The variational stability of periodic solutions is examined using an extension of the Floquet theory to a fourth order system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229517
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  • 7
    Electronic Resource
    Electronic Resource
    An alternate transition from the Lagrangian of a satellite to equations of motion (1988)
    Springer
    Celestial mechanics and dynamical astronomy 45 (1988), S. 333-386 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A procedure is outlined for a conservative system which makes it possible to go from a Lagrangian of a librating system to the corresponding equations of motion in the Eulerian form. The transition does not require a choice of rotational coordinates and makes use of angular velocities and direction cosines directly. The procedure thus synthesizes attractive features of two classical approaches and has far reaching consequences: it is particularly useful in formulating equations of motion for complex flexible systems of contemporary interest. For the case of a satellite with two flexible plate-type appendages, for example, the approach reduced the formulation time to one-third. The basic mathematical concepts are briefly touched upon in the beginning which help explain the subsequent development.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01245758
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  • 8
    Electronic Resource
    Electronic Resource
    A general formulation for the nonlinear dynamics and control of orbiting flexible structures (1993)
    Springer
    Computational mechanics 13 (1993), S. 204-230 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A relatively general Lagrangian formulation for studying the dynamics of a large class of spacecraft characterized by interconnected flexible members forming a tree topology, is presented. Methodology and development of the computer code suitable for parametric dynamical study and control are briefly outlined. Versatility of the general formulation is demonstrated through dynamics studies of the Permanently Manned Configuration (PMC) of the proposed Space Station Freedom and the slewing dynamics and control of the two-link Mobile Servicing System (MSS) aboard Freedom. The PMC study indicates the effect of flexibility cannot be overlooked. Even a small disturbance on the main or stinger can result in unacceptable magnitudes of velocity and acceleration. The MSS study compares the system response subjected to the InPlane (IP) and Out-of-Plane (OP) maneuvers. Results indicate that, without control, the OP maneuver excites large yaw motion of the Space Station. Consequently, the OP maneuver has a large pointing error. Nonlinear control, based on the Feedback Linearization Technique, appears promising. By controlling the librational motion of the station, the performance of the OP maneuver improves significantly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370136
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  • 9
    Electronic Resource
    Electronic Resource
    A numerical analysis of the unsteady flow past bluff bodies (1990)
    Springer
    Computational mechanics 6 (1990), S. 11-34 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper describes in detail a relatively sophisticated numerical approach, using the Boundary Element Method in conjunction with the Discrete Vortex Model, to represent the complex unsteady flow field around a bluff body with separating shear layers. Important steps in the numerical analysis of this challenging problem are discussed and a performance evaluation algorithm established. Of considerable importance is the effect of computational parameters such as number of elements representing the geometry, time-step size, location of the nascent vortices, etc., on the accuracy of results and the associated cost. As an example, the method is applied to the analysis of the flow around a stationary Savonius rotor. A detailed parametric study provides fundamental information concerning the starting torque time histories, evolution of the wake, Strouhal number, etc. A comparison with the wind tunnel test data shows remarkable correlation suggesting considerable promise for the approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00373796
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  • 10
    Electronic Resource
    Electronic Resource
    Order-N Formulation and Dynamics of Multi-Unit Flexible Space Manipulators (1998)
    Springer
    Nonlinear dynamics 17 (1998), S. 347-368 
    Details
    ISSN: 1573-269X
    Keywords: order-N formulation ; variable
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract As robotic manipulators gain more importance in space operations, it is becoming imperative to understand their distinctive dynamics and control characteristics. With the increasing complexity of space robots, efficient algorithms are now required for their simulation. The present study uses an order-N algorithm, based on the Lagrangian approach and velocity transformations, to simulate the planar dynamics of a novel orbiting manipulator with arbitrary number of slewing and deployable flexible links. The relatively general formulation accounts for interactions between orbital, librational, slewing, deployment, and vibrational degrees of freedom, and thus is applicable to a large class of manipulator systems of contemporary interest. A parametric analysis of the system dynamics is carried out to investigate the effects of initial disturbances, variation of system parameters and maneuver profiles. The study suggests significant coupling between the rigid body motion and structural vibrations. As a result, the system's flexibility can significantly affect the manipulator's performance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008314211138
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