论文标题
中央力场的恒定坡道
Constant-speed ramps for a central force field
论文作者
论文摘要
我们调查了确定质量$ m $的粒子以恒定速度移动的坡道的平面曲线的问题，其何时受到摩擦力的作用，而其幅度$ f（r）$仅取决于距离距离的距离$ r $。在本文中，我们描述了$ f（r）= - m/r $的所有恒定坡道。我们展示了圆圈，对数螺旋起着重要的作用。他们不仅是解决方案，而且其他所有解决方案都可以接近圆形或对数螺旋。
We investigate the problem of determining the planar curves that describe ramps where a particle of mass $m$ moves with constant-speed when is subject to the action of the friction force and a force whose magnitude $F(r)$ depends only on the distance $r$ from the origin. In this paper we describe all the constant-speed ramps for the case $F(r)=-m/r$. We show the circles and the logarithmic spirals play an important role. No only they are solutions but every other solution approaches either a circle or a logarithmic spiral.
