摘要
本文分别研究了质量均匀分布的硬币在粗糙水平面上沿直线滚动和在粗糙斜面上滚动时的质心速度与接触点的移动速度.本文还以X,Y,θ,φ,ψ为广义坐标,给出了硬币作横向转动时的拉格朗日算符,得到了相应的拉格朗日方程.并由此出发,得到了沿直线滚动时硬币处于稳定状态的条件为n^2>g/3R,作横向转动时硬币处于稳定状态的条件为φ~2>4g/R.
This paper makes a research on the velocities of the mass center and the contact point for the coin with homogeneous mass distribution, which rolls along the rectiline on the rough horizontal plane and the rough inclined plane. It also supplies the Lagrangian operator and the Lagrangian equations for the cross rotation of the coin. Thus the conditions for the rectilinear rolling and for the cross rotation are obtained, under which the motions of the coin are stable.
关键词
硬币
转动
稳定性
质心
速度
velocity of the mass center
cross rotation
incomplete system
generalized coordinates
stability
