The global flow of the parabolic restricted three-body problem
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We have two mass points of equal masses m1=m2 > 0 moving under Newton’s law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We consider a third mass point, of mass m3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their center of mass. Since m3=0, the motion of m1 and m2 is not affected by the third and from the symmetry of the motion it is clear that m3 will remain on the line L. The parabolic restricted three-body problem describes the motion of m3. Our main result is the characterization of the global flow of this problem.
Keywordsglobal flow restricted three-body problem Sitnikov problem
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- Alekseev, V. M.: 1968, ‘Quasirandom dynamical systems I, II, II’, Math. USSR Sbornik, 5, 73–128, 1968, 6: 505–560, 1968, 7: 1–43, 1969.Google Scholar
- Cors, J. M., Llibre, J. 1996aQualitative study of the parabolic collision restricted three-body problemContemporary Math198119Google Scholar
- Llibre, J., Simo, C. 1980‘Qualitative study of the Sitnikov problem’, PublSec. Mat. Univ. Autònoma Barcelona184971Google Scholar
- Meyer, R. K., Wang, Q. 1993Global phase structure of the restricted isosceles three-body problem with positive energyTrans. Am. Math. Soc.338311336Google Scholar
- Moser, J. 1973‘Stable and Random Motions in Dynamical Systems with Special Emphasis on Celestial Mechanics’Annals of Mathematics Studies Number 77 Princeton University PressNew JerseyGoogle Scholar
- Pollard, H. 1996‘Mathematical Introduction to Celestial Mechanics’Prentice-Hall Inc. New JerseyGoogle Scholar
- Siegel, C. L., Moser, J.K. 1995‘Lectures on Celestial Mechanics’Springer-VerlagBerlinGoogle Scholar
- Wang, Q. 1986Qualitative study of n-body problem: unitized momentum transformation and its application restricted isosceles three-body problem with positive energyBhatnagar, K. B. eds. Space Dynamics and Celestial Mechanics ReidelDordrecht6169Google Scholar