水平面上有限厚度刚性圆盘的定常运动
Steady Motion of a Rigid Disk of Finite Thickness on a Horizontal Plane
摘要：
本文讨论了有限厚度刚性圆盘在重力作用下在水平面上作边缘滚动的定常运动。的控制方程，并考虑两种情况下，允许一个稳定的状态下的解决方案：滚动一贯粗糙的地面和滚动完全光滑的地面。对这两种地基，导出了稳定运动的条件，并指出圆盘的可能稳定运动是在圆内的直线上。还讨论了稳态附近的振荡，并建立了稳定运动的条件。
英文摘要：
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line in a circle. Also oscillations about steady state are discussed and conditions for stable motion are established.
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