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Shiqing Zhang

Publications and source records attributed to Shiqing Zhang.

50 records · Page 3Linked to original sources
arXiv2013

Periodic Solutions for Circular Restricted 4-body Problems with Newtonian Potentials

We study the existence of non-collision periodic solutions with Newtonian potentials for the following planar restricted 4-body problems: Assume that the given positive masses $m_{1},m_{2},m_{3}$ in a Lagrange configuration move in circular obits around their center of masses, the sufficiently small mass moves around some body. Using variational minimizing methods, we prove the existence of minimizers for the Lagrangian action on anti-T/2 symmetric loop spaces. Moreover, we prove the minimizers are non-collision periodic solutions with some fixed wingding numbers.

math-ph↗
arXiv2012

Nonplanar Periodic Solutions for Spatial Restricted 3-Body and 4-Body Problems

In this paper, we study the existence of non-planar periodic solutions for the following spatial restricted 3-body and 4-body problems: for $N=2 or 3$, given any masses $m_{1},...,m_{N}$, the mass points of $m_{1},...,m_{N}$ move on the $N$ circular obits centered at the center of masses, the sufficiently small mass moves on the perpendicular axis passing the center of masses. Using variational minimizing methods, we establish the existence of the minimizers of the Lagrangian action on anti-T/2 or odd symmetric loop spaces. Moreover, we prove these minimizers are non-planar periodic solutions by using the Jacobi's Necessary Condition for local minimizers.

math-ph↗
arXiv2012

Existence of Hyperbolic Orbits for N-body Type Problems

In this paper, we use variational minimizing method to prove the existence of hyperbolic solution with a prescribed positive energy for N-body type problems with strong forces. Firstly, we get periodic solutions using suitable constraints, then by taking limit about a sequence of periodic solutions, we get the hyperbolic orbits.

math-ph↗
arXiv2012

Nonplanar Periodic Solutions for Spatial Restricted N+1-Body Problems

We use variational minimizing methods to study spatial restricted N+1-body problems with a zero mass moving on the vertical axis of the moving plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric loop space must be a non-planar periodic solution for any $N\geq2$.

math-ph↗
arXiv2012

Planar Symmetric Concave Central Configurations in Four-body Problem

In this paper, we consider the problem: given a symmetric concave configuration of four bodies, under what conditions is it possible to choose positive masses which make it central. We show that there are some regions in which no central configuration is possible for positive masses. Conversely, for any configuration in the complement of the union of these regions, it is always possible to choose positive masses to make the configuration central.

math-ph↗
arXiv2012

6-Body Central Configurations Formed by Two Isosceles Triangles

In this paper,we show the existence of a class of 6-body central configurations with two isosceles triangles; which are congruent to each other and keep some distance.We also study the necessary conditions about masses for the bodies which can form a central configuration.

math-ph↗
arXiv2012

Stacked Central Configurations for Newtonian N+4-Body Problems

In this paper,we study spatial central configurations where N bodies are at the vertices of a regular N-gon $T$ and the other 4 bodies are symmetrically located on the straight line that is perpendicular to the plane that contains $T$ and passes through the center of $T$.We study the necessary conditions about masses for the bodies which can form a central configuration and show the existence of central configurations for Newtonian N+4-body problems.

math-ph↗
arXiv2011

Large Lagrangian Actions on Elliptical Solutions of 2-Body and 3-Body Problems with Fixed Energies

Based on the works of Gordon ([4]) and Zhang-Zhou([8])) 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-Coti Zelati ([1]) to compute the Lagrangian actions on Keplerian and Lagrangian elliptical solutions with fixed energies, we also find an interesting relationship between period and energy for Lagrangian elliptical solutions with Newtonian potentials.

math-ph↗