Inverse problem of central configurations and singular curve in the collinear 4-body problem

Details Inverse problem of central configurations and singular curve in the collinear 4-body problem Inverse problem of central configurations and singular curve in the collinear 4-body problem

Jul 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cemda.107..353x&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 107, Issue 3, pp.353-376

Astronomy and Astrophysics

Astronomy

2

Scientific paper

In this paper, we consider the inverse problem of central configurations of n-body problem. For a given {q=(q_1, q_2, ldots, q_n)in ({R}^d)^n}, let S( q) be the admissible set of masses denoted { S(q)=\{ m=(m_1,m_2, ldots, m_n)| m_i in {R}^+, q} is a central configuration for m}. For a given {min S(q)}, let S m ( q) be the permutational admissible set about m = ( m 1, m 2, . . . , m n ) denoted S_m(q)=\{m^' | m^'in S(q),m^' not=m and m^' {is a permutation of } m \}. The main discovery in this paper is the existence of a singular curve {bar{Γ}_{31}} on which S m ( q) is a nonempty set for some m in the collinear four-body problem. {bar{Γ}_{31}} is explicitly constructed by a polynomial in two variables. We proved:
(1)
If {min S(q)}, then either # S m ( q) = 0 or # S m ( q) = 1.

Affiliated with

Also associated with

No associations

Rating

Inverse problem of central configurations and singular curve in the collinear 4-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 Inverse problem of central configurations and singular curve in the collinear 4-body problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inverse problem of central configurations and singular curve in the collinear 4-body problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-955906