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. Not only they are solutions but every other solution approaches either a circle or a logarithmic spiral.

中文翻译：

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用于中心力场的等速斜坡

我们研究确定确定描述斜坡的平面曲线的问题，在该斜坡上，质量$ m $的粒子在受到摩擦力和大小$ F（r）$仅取决于摩擦力的作用时将以恒定速度运动。与原点的距离$ r $。在本文中，我们描述了情况$ F（r）= -m / r $时的所有恒速斜坡。我们显示了圆圈和对数螺旋起着重要作用。它们不仅是解决方案，而且所有其他解决方案都接近圆或对数螺旋。