We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutual repulsive, as in the two- or multi-electron atomic case or mutually attractive, as in the planetary-orbit case. Specifically, we have devised a mathematical framework for causing deterministic collisions by launching an inner orbiting body to a higher energy such that this inner body is guaranteed to collide with the outer body. Our method first expresses the problem mathematically as coupled nonlinear differential equations with a time-dependent driving force and solve to find a feasible solution for the force function. Although our calculation is based strictly on classical physics, our approach is suitable for the case of Helium with two highly excited electrons and is also valid for creating collisions in the gravitational case such as for our solar system.

中文翻译：

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在两个绕行物体之间产生确定性碰撞

我们的目标是通过对一个或两个物体施加与时间相关的外力，从而在轨道物体之间产生确定性的碰撞，无论该物体是相互排斥的（如在双电子原子或多电子原子的情况下，还是相互吸引的，如在行星电子中）轨道情况。具体来说，我们设计了一个数学框架，通过向内部轨道的物体发射更高的能量来引起确定性碰撞，从而确保该内部物体与外部物体碰撞。我们的方法首先将该问题数学表示为具有时间相关驱动力的非线性非线性微分方程，然后求解以找到力函数的可行解。尽管我们的计算严格基于经典物理学，