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  • 1
    Electronic Resource
    Electronic Resource
    A complex analytic solution for the attitude motion of a near-symmetric rigid body under body-fixed torques (1991)
    Springer
    Celestial mechanics and dynamical astronomy 51 (1991), S. 281-301 
    Details
    ISSN: 1572-9478
    Keywords: Analytic solutions ; rigid body motion ; kinematics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Although analytic solutions for the attitude motion of a rigid body are available for several special cases, a comprehensive theory does not exist in the literature for the more complicated problems found in spacecraft dynamics. In the present paper, analytic solutions in complex form are derived for the attitude motion of a near-symmetric rigid body under the influence of constant body-fixed torques. The solution is very compact, which enables efficient and rapid machine computation. Numerical simulations reveal that the solution is very accurate when applied to typical spinning spacecraft problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051695
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Suboptimal Control of Rigid Body Motion with a Quadratic Cost (1998)
    Springer
    Dynamics and control 8 (1998), S. 55-81 
    Details
    ISSN: 1573-8450
    Keywords: Rigid body ; quadratic cost ; Lyapunov functions ; Linear matrix inequalities ; stabilization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008278929841
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal Control of Rigid Body Angular Velocity with Quadratic Cost (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 507-532 
    Details
    ISSN: 1573-2878
    Keywords: Rigid bodies ; Hamilton–Jacobi equation ; Riccati equation ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by the Euler equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal controllers. These controllers have a very simple structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022656326640
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Global Asymptotic Stabilization of a Spinning Top With Torque Actuators Using Stereographic Projection (1997)
    Springer
    Dynamics and control 7 (1997), S. 215-233 
    Details
    ISSN: 1573-8450
    Keywords: spinning top ; stabilization ; stereographic projection ; Lyapunov function ; Hamilton-Jacobi theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The dynamical equations for a spinning top are derived in which theorientation is specified by a complex variable using stereographic projectionof Poisson's equations. Necessary and sufficient conditions for Lyapunovstability of the uncontrolled motion of the spinning top are derived usingthe Energy-Casimir method. Control laws that globally asymptoticallystabilize the spinning top to the sleeping motion using two torque actuatorsare synthesized by employing techniques from the theory of systems in cascadeform and generalized using Hamilton-Jacobi-Bellman theory with zero dynamics.In short, this paper provides a nice example where the interplay betweendynamics and control leads to elegant and powerful results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008238115854
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    Paper (German National Licenses)
    Fulltext
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