We investigate the central configurations of the restricted <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$1+N$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>+</mo> <mi>N</mi> </mrow> </math></EquationSource> </InlineEquation>-body problem, in which N bodies are infinitesimal and the remaining one is dominant. Assuming that the distances between the i-th and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$(i+1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-th infinitesimal bodies are identical for all <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$i=1,2,\ldots ,N-1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, we establish the following results: (1) For <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$N = 4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>, there exist two distinct equidistant central configurations: a square and a special isosceles trapezoid; (2) For <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$N\ge 4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> with all infinitesimal bodies of equal mass, the only possible equidistant central configuration is a regular polygon.

Equidistant central configuration for the restricted $1+N$-body problem

期刊论文
发表日期：

2026年6月15日

查看全文

Jian Chen,
Ying Han,
Jie Lv,
Junyu Hou,
Mingfang Yang

摘要

We investigate the central configurations of the restricted $1+N$ $1 + N$ -body problem, in which N bodies are infinitesimal and the remaining one is dominant. Assuming that the distances between the i-th and $(i+1)$ $(i + 1)$ -th infinitesimal bodies are identical for all $i=1,2,\ldots ,N-1$ $i = 1, 2, \dots, N - 1$ , we establish the following results: (1) For $N = 4$ $N = 4$ , there exist two distinct equidistant central configurations: a square and a special isosceles trapezoid; (2) For $N\ge 4$ $N \geq 4$ with all infinitesimal bodies of equal mass, the only possible equidistant central configuration is a regular polygon.

Equidistant central configuration for the restricted \(1+N\)-body problem

摘要