On some exceptional cases in the integrability of the three-body problem

Details On some exceptional cases in the integrability of the three-body problem On some exceptional cases in the integrability of the three-body problem

2006-10-31

arxiv.org/abs/math/0610951v1

Mathematics

Dynamical Systems

7 pages

Scientific paper

10.1007/s10569-007-9086-5

We consider the Newtonian planar three--body problem with positive masses $m_1$, $m_2$, $m_3$. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian orbit besides three exceptional cases $ \sum m_i m_j/(\sum m_k)^2= 1/3$, $2^3/3^3$, $2/3^2$ where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis of the three-body problem started in our previous papers and based of the Morales-Ramis-Ziglin approach.

Affiliated with

Also associated with

No associations

Rating

On some exceptional cases in the integrability of the three-body problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On some exceptional cases in the integrability of the three-body problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some exceptional cases in the integrability of the three-body problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47414