caa a22 4500 467987270 CHVBK 20180323112535.0 cr unu---uuuuu 170328e19901201xx s 000 0 eng 10.1007/BF02426678 doi (NATIONALLICENCE)springer-10.1007/BF02426678 Hamiltonian dynamics of a rigid body in a central gravitational field [Elektronische Daten] [Li-Sheng Wang, P. Krishnaprasad, J. Maddocks] 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. Kluwer Academic Publishers, 1991 Hamiltonian mechanics nationallicence relative equilibrium nationallicence rigid body dynamics nationallicence Wang Li-Sheng Electrical Engineering Department & Systems Research Center, University of Maryland, 20742, College Park, MD aut Krishnaprasad P. Electrical Engineering Department & Systems Research Center, University of Maryland, 20742, College Park, MD aut Maddocks J. Mathematics Department, University of Maryland, 20742, College Park, MD aut Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 50/4(1990-12-01), 349-386 0923-2958 50:4<349 1990 50 10569 https://doi.org/10.1007/BF02426678 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02426678 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Li-Sheng Electrical Engineering Department & Systems Research Center, University of Maryland, 20742, College Park, MD aut NATIONALLICENCE 700 1- Krishnaprasad P. Electrical Engineering Department & Systems Research Center, University of Maryland, 20742, College Park, MD aut NATIONALLICENCE 700 1- Maddocks J. Mathematics Department, University of Maryland, 20742, College Park, MD aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 50/4(1990-12-01), 349-386 0923-2958 50:4<349 1990 50 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer