Horseshoes and nonintegrability in the restricted case of a spinless axisymmetric rigid body in a central gravitational field |
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Authors: | Radu Balan |
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Institution: | (1) Program in Applied and Computational Mathematics, Princeton University, 08544 Princeton, NJ, USA |
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Abstract: | The purpose of this paper is to study the motion of a spinless axisymmetric rigid body in a Newtonian field when we suppose the motion of the center of mass of the rigid body is on a Keplerian orbit. In this case the system can be reduced to a Hamiltonian system with configuration space of a two-dimensional sphere. We prove that the restricted planar motion is analytical nonintegrable and we find horseshoes due to the eccentricity of the orbit. In the caseI
3/I
1>4/3, we prove that the system on the sphere is also analytical nonintegrable.On leave from the Polytechnic Institute of Bucharest, Romania. |
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Keywords: | Horseshoes analytic integrability rigid body problem |
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