论文标题
在线性抑制2个身体问题上
On a linearly damped 2 body problem
论文作者
论文摘要
确定性的卢瑟福 - 博原子模型中两个单个行星的两个运动的通常方程式是保守的，其起源具有奇异的潜力。当添加耗散时，会出现新现象。结果表明，每当动量不是零时，即使在允许任意较大的速度的经典环境中，移动粒子也不会在有限的时间内到达中心，并且其位移也不会爆炸。 此外，我们证明，所有有限的解决方案都倾向于$ 0 $，对于$ t $，一些正式的计算表明，存在具有渐近螺旋的特殊轨道，这些轨道与中心呈渐近螺旋式呈指数级的快速收敛。
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. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in finite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover we prove that all bounded solutions tend to $0$ for $t$ large, and some formal calculations suggest the existence of special orbits with an asymptotically spiraling exponentially fast convergence to the center.
