Abstract

We consider a system consisting of a platform moving translationally along a fixed straight line in the presence of the viscous friction force and a body making a given translational motion along the same straight line relative to the platform due to internal forces. In relative motion, the value of the body velocity is bounded. It is proved that in the case of linear viscous friction, unlimited displacement of the platform in any direction is impossible. In the general case, under certain conditions imposed on the viscous friction force, the value of the velocity of the platform is bounded. In this case, if the displacement of the platform in any direction, e.g., to the right, is not limited, then the value of the velocity of the platform changes its sign an infinite number of times over time, and the total time of the platform’s motion to the left and the distance traveled tend to infinity.

中文翻译：

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存在外部黏性摩擦的内部元件正在运动的系统的运动

摘要

我们考虑一个系统，该系统包括一个平台，该平台在存在粘性摩擦力的情况下沿着固定的直线平移，而一个主体由于内力而沿着同一直线相对于该平台进行给定的平移运动。在相对运动中，身体速度的值是有界的。已经证明，在线性粘性摩擦的情况下，平台在任何方向上的无限位移都是不可能的。在一般情况下，在施加于粘滞摩擦力的某些条件下，平台速度的值是有界的。在这种情况下，如果平台在任何方向（例如，向右）上的位移不受限制，则平台速度的值会随着时间的推移无限次数地改变其符号，