Shiqing Zhang

Four-body central configurations with adjacent equal masses

Abstract For any convex non-collinear central configuration of the planar Newtonian 4-body problem with adjacent equal masses m 1 = m 2 ≠ m 3 = m 4 , with equal lengths for the two diagonals, we prove it must possess a symmetry and must be an isosceles trapezoid; furthermore, which is also an isosceles trapezoid when the length between m 1 and m 4 equals the length between m 2 and m 3 .

Central configurations formed by two twisted regular polygons

In this paper, we study the necessary conditions and sufficient conditions for the central configurations formed by two twisted regular polygons (one N-regular polygon and one L-regular polygon). We wish to extend the results of the symmetrical central configurations formed by two twisted N-regular polygons, however, it will be proved that there are not more central configurations in a more general setting than the central configurations considered for some more particular situations before.

Lagrangian actions for elliptical solutions of 2-body and 3-body problems with fixed energies

Abstract Based on the works of Gordon (1977) and Zhang and Zhou (2001) on the variational minimizing properties for Keplerian orbits and Lagrangian solutions of Newtonian 2-body and 3-body problems, we use the constrained variational principle of Ambrosetti and Coti Zelati (1990) to compute the Lagrangian actions on Keplerian and Lagrangian elliptical solutions with fixed energies. We also find an interesting relation between the period and the energy for Lagrangian elliptical solutions with Newtonian potentials.