Some new dynamical effects in the perturbed Euler-Poinsot problem, due to splitting of separatrices. (English. Russian original) Zbl 0722.70005
J. Appl. Math. Mech. 53, No. 2, 165-173 (1989); translation from Prikl. Mat. Mekh. 53, No. 2, 215-225 (1989).
Summary: An investigation is presented of a series of new qualitative dynamical effects, due to the phenomenon of the splitting of the asymptotic surfaces (separatrices) of perturbed permanent rotations in the motion of an asymmetric rigid body with fixed point in a weak gravitational field (or, in greater generality, an axisymmetric irrotational field). A quantitative index of the non-coincidence of the separatrices is defined and appropriate estimates are established. Conditions are found which, when imposed on the parameters of the problem, imply the existence of invariant tori separating perturbed hyperbolic permanent rotations. It is shown that for almost all values of the parameters there exist quasirandom motions due the existence of transversally intersecting separatrices. Bifurcation effects, represented by infinitely many changes in the qualitative behaviour pattern of the trajectories as the Poincaré parameter tends to zero, are observed and studied. This paper is a continuation of the author’s paper [ibid. 51, No.3, 363-370 (1987; Zbl 0653.70008)].
MSC:
| 70E20 | Perturbation methods for rigid body dynamics |
| 70E15 | Free motion of a rigid body |
| 37G99 | Local and nonlocal bifurcation theory for dynamical systems |
Keywords:
dynamical effects; splitting of the asymptotic surfaces; perturbed permanent rotations; weak gravitational field; existence of invariant tori; transversally intersecting separatrices; Poincaré parameterCitations:
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