The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear which were investigated thoroughly by R. Ortega and his co-authors between 2014 and 2017, in particular all solutions are bounded and tend to $ 0 $ for $ t $ large, some of them with asymptotically spiraling exponentially fast convergence to the center. We provide explicit estimates for the bounds in the general case that we refine under specific restrictions on the initial state, and we give a formal calculation which could be used to determine practically some special asymptotically spiraling orbits. Besides, a related model with exponentially damped central charge or mass gives some explicit exponentially decaying solutions which might help future investigations. An atomic contraction hypothesis related to the asymptotic dying off of solutions proven for the dissipative model might give a solution to some intriguing phenomena observed in paleontology, familiar electrical devices and high scale cosmology.

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关于一些受挫的 2 身体问题

在确定性卢瑟福-玻尔原子模型中，单个行星绕太阳运动和电子的常用方程是保守的，原点具有奇异势。当添加耗散时，会出现新现象，R. Ortega 及其合著者在 2014 年至 2017 年间对其进行了彻底调查，特别是所有解都是有界的，并且趋向于 $ 0 $ 大 $ t $，其中一些具有渐近性螺旋式指数级快速收敛到中心。我们在一般情况下提供明确的边界估计，我们在初始状态的特定限制下进行细化，并且我们给出了一个正式的计算，该计算可用于实际上确定一些特殊的渐近螺旋轨道。除了，具有指数阻尼中心电荷或质量的相关模型给出了一些明确的指数衰减解，这可能有助于未来的研究。与耗散模型证明的解决方案渐近消亡相关的原子收缩假设可能会为古生物学、熟悉的电子设备和大规模宇宙学中观察到的一些有趣现象提供解决方案。