哪位大大帮我把下面的翻译成英文本文运用了8-体问题的正四面形套中心构型来研究中心构型在伸缩变换和正交变换下的变化,并在此基础上推断构成正四面形套中心构型的充分必要条件及其

Question

哪位大大帮我把下面的翻译成英文
本文运用了8-体问题的正四面形套中心构型来研究中心构型在伸缩变换和正交变换下的变化,并在此基础上推断构成正四面形套中心构型的充分必要条件及其在任意的正数 下的等价类.
注：
8-体问题：8-body problems
中心构型：central configurations
正四面形套：nested regular tetrahedrons

Answer 1

This paper USES the 8 - body problem is all form sets of central configurations to research center in rsa telescopic transformation and orthogonal transform changes,and on this basis infer that constitute are all form set of central configurations in the necessary and sufficient conditions under arbitrary positive of equivalence.
8 - body problem:8 - life-time body
Central configurations:central configurations
Are all regular tetrahedrons nested fractal set