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  • rigid body dynamics  (2)
  • Adaptive control  (1)
  • stability  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 269-298 
    ISSN: 1572-9222
    Keywords: Geometric mechanics ; reduction ; stability ; chaos ; rigid body dynamics ; periodic orbits ; 58F
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 50 (1990), S. 349-386 
    ISSN: 1572-9478
    Keywords: Hamiltonian mechanics ; relative equilibrium ; rigid body dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper concerns the dynamics of a rigid body of finite extent moving under the influence of a central gravitational field. A principal motivation behind this paper is to reveal the hamiltonian structure of the n-body problem for masses of finite extent and to understand the approximation inherent to modeling the system as the motion of point masses. To this end, explicit account is taken of effects arising because of the finite extent of the moving body. In the spirit of Arnold and Smale, exact models of spin-orbit coupling are formulated, with particular attention given to the underlying Lie group framework. Hamiltonian structures associated with such models are carefully constructed and shown to benon-canonical. Special motions, namely relative equilibria, are investigated in detail and the notion of anon-great circle relative equilibrium is introduced. Non-great circle motions cannot arise in the point mass model. In our analysis, a variational characterization of relative equilibria is found to be very useful. Thereduced hamiltonian formulation introduced in this paper suggests a systematic approach to approximation of the underlying dynamics based on series expansion of the reduced hamiltonian. The latter part of the paper is concerned with rigorous derivations of nonlinear stability results for certain families of relative equilibria. Here Arnold's energy-Casimir method and Lagrange multiplier methods prove useful.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-9686
    Keywords: Self-tuning controller ; Drug infusion ; Adaptive control ; Nitroprusside
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A self-tuning controller was implemented for the automated infusion of sodium nitroprusside to lower mean arterial pressure in anesthetized dogs. The system incorporated a recursive least-squares parameter identifier and a modified minimumvariance controller. The onset delay was estimated on-line, the performance criterion included the cost of control, and requested step-changes were automatically translated into five successive smaller steps to reduce overshoot. The performance of the system in lowering mean arterial pressure was quantitatively compared with that of a well-trained anesthesiologist. In 10 runs in four animals, the automated system performed as well as the physician who devoted 100% of his attention to the task. Since the stability of the self-tuning controller cannot be guaranteed, such a system should be operated only in the presence of appropriate supervisory algorithms.
    Type of Medium: Electronic Resource
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