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101.
Li-Sheng Wang P. S. Krishnaprasad J. H. Maddocks 《Celestial Mechanics and Dynamical Astronomy》1990,50(4):349-386
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.
This work was supported in part by the AFOSR University Research Initiative Program under grant AFOSR-87-0073, by AFOSR grant
89-0376, and by the National Science Foundation's Engineering Research Centers Program: NSFD CDR 8803012. The work of P.S.
Krishnaprasad was also supported by the Army Research Office through the Mathematical Sciences Institute of Cornell University. 相似文献
102.
Normalization of a perturbed elliptic oscillator, when executed in Lissajous variables, amounts to averaging over the elliptic anomaly. The reduced Lissajous variables constitute a system of cylindrical coordinates over the orbital spheres of constant energy, but the pole-like singularities are removed by reverting to the subjacent Hopf coordinates. The two-parameter coupling that is a polynomial of degree four admitting the symmetries of the square is studied in detail. It is shown that the normalized elliptic oscillator in that case behaves everywhere in the parameter plane like a rigid body in free rotation about a fixed point, and that it passes through butterfly bifurcations wherever its phase flow admits non isolated equilibria. 相似文献
103.
F. Varadi C. M. De La Barre W. M. Kaula M. Ghil 《Celestial Mechanics and Dynamical Astronomy》1995,62(1):23-41
New techniques to study Hamiltonian systems with Hamiltonian forcing are proposed. They are based on singularly weighted symplectic forms and transformations which preserve these forms. Applications pertaining to asteroid motion are outlined. These involve the presence of both Jupiter and Saturn. 相似文献
104.
Relations are established between the Delaunay variables defined over a phase space E in four dimensions and the Lissajous variables defined over a four-dimensional phase space F when the latter is mapped onto E by a parabolic canonical transformation. 相似文献