论文标题
体积变量的经典$ n $体系统。 ii。四体情况
Classical $n$-body system in volume variables. II. Four-body case
论文作者
论文摘要
显然，可以用四面体的顶点来识别$ d> 2 $尺寸空间中4个尸体的位置。四面体的平方，四个方面的平方区域的加权总和和平方边缘的加权总和称为体积变量。仅考虑依赖体积变量的一个翻译不变电位的家族以及仅取决于体积变量的牛顿方程的解决方案。对于零角动量$ l = 0 $的情况，描述这些解决方案的相应哈密顿量将得出。 Three examples are studied in detail: (I) the (super)integrable 4-body closed chain of harmonic oscillators for $d>2$ (the harmonic molecule), (II) a generic, two volume variable dependent potential whose trajectories possess a constant moment of inertia ($d>1$), and (III) the 4-body anharmonic oscillator for $d \geq 1$.这项工作是续集的第二部：第一个[IJMPA 36，第18号（2021）]专门研究体积变量中的三体经典问题。
It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges are called the volume variables. A family of translation-invariant potentials which depend on volume variables alone is considered as well as solutions of the Newton equations which solely depend on volume variables. For the case of zero angular momentum $L=0$ the corresponding Hamiltonian, which describes these solutions, is derived. Three examples are studied in detail: (I) the (super)integrable 4-body closed chain of harmonic oscillators for $d>2$ (the harmonic molecule), (II) a generic, two volume variable dependent potential whose trajectories possess a constant moment of inertia ($d>1$), and (III) the 4-body anharmonic oscillator for $d \geq 1$. This work is the second of the sequel: the first one [IJMPA 36, No. 18 (2021)] was dedicated to study the 3-body classical problem in volume variables.
