The general Jacobi symplectic variables generated by a combinatorial algorithm from the full binary tree T(N) are used to formulate some nonheliocentric gravitational N-body problems in perturbation form. The resulting uncoupled term H_U for (N - 1) independent Keplerian motions and the perturbation term U_P are both explicitly dependent on the partial ordering induced by the tree T(N). This leads to suitable conditions on separations of the N bodies for the perturbation to be small. We prove the Herman resonance for a new approximation of the 5-body problem. Full details of the derivations of the perturbation form and Herman resonance are given only in the case of five bodies using the caterpillar binary tree T_c(5).

中文翻译：

---

Jacobi的一般坐标和Herman共振对一些非螺旋中心天体N体问题的影响

通过组合算法从完整的二叉树T（N）生成的一般Jacobi辛变量用于以摄动形式表述一些非Heliocentric重力N体问题。对于（N -1）个独立的Keplerian运动，所得的解耦项H _U和扰动项U _P都明确取决于树T（N）引起的偏序。这导致分离N的合适条件身体的摄动要小。我们证明了5体问题的新近似的Herman共振。仅在使用履带二叉树T _c（5）的五个物体的情况下，才给出了扰动形式和Herman共振的推导的完整细节。