The motion of Chaplygin’s skate on a horizontal plane with dry friction is considered. It is assumed that the friction force depends on an angle between the sliding velocity and the plane of the skate. It is shown that the time of the skate sliding can be found from a transcendental equation and depends on the initial values of the angular velocity, the sliding velocity, and the angle between the sliding velocity and the plane of the skate. A countable set of initial values of the sliding velocity such that the sliding time does not depend on this angle is found.

中文翻译：

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Chaplygin滑冰在具有各向异性干摩擦的水平面上的动力学

查普利金（Chaplygin）溜冰鞋在具有干摩擦的水平面上的运动被考虑。假定摩擦力取决于滑动速度和冰鞋平面之间的角度。结果表明，滑冰滑行的时间可以从一个先验方程中找到，并且取决于角速度，滑行速度以及滑行速度与滑冰机平面之间的夹角的初始值。找到了一组可计数的滑动速度初始值，以使滑动时间不依赖于该角度。