三体问题部分平均牛顿位势的首次积分
A first integral to the partially averaged Newtonian potential of the three-body problem
摘要：
我们考虑部分平均，即，拉格朗日平均相对于{ \it只是一个}的两个平均异常，牛顿部分的扰动函数在三体问题的哈密顿量。我们证明了这样的部分平均值具有非平凡的首次积分。我们表明，这个积分是完全负责的某些取消的平均牛顿位势，包括财产注意到哈林顿在60年代。我们还强调其联合作用（连同某些对称性）在所谓的“赫尔曼共振”的外观。最后，我们讨论了一个应用程序和一个开放的问题。
英文摘要：
We consider the partial average i.e., the Lagrange average with respect to {\it just one} of the two mean anomalies, of the Newtonian part of the perturbing function in the three--body problem Hamiltonian. We prove that such a partial average exhibits a non--trivial first integral. We show that this integral is fully responsible of certain cancellations in the averaged Newtonian potential, including a property noticed by Harrington in the 60s. We also highlight its joint rôle (together with certain symmetries) in the appearance of the so called "Herman resonance". Finally, we discuss an application and an open problem.
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