关键词: 刚体力学, 线性近似, 无量纲化, 不动点, 阻尼振荡

Abstract: Currently, in the undergraduate teaching process, particularly in the field of physics, the emphasis is mainly on presenting “perfect” scientific principles and solvable exercises. However, it is precisely those unsolvable problems that can reflect students’ understanding of the entire issue and stimulate their creativity. This paper provides an indepth analysis of a rigid body problem in the 39th National Physics Competition for high school students (alternate paper) and combines it with numerical calculations. It is found that when the initial angular speed of ball D is very small, the result given by the original reference answer is reasonable. In addition, the oscillating phenomenon of ball A’s angular velocity as the increasement of initial speed of ball D is studied. According to the analysis of fixed points, the critical initial speed at which linear evolution to damped oscillation is estimated. Some peculiar phenomena that occur during the evolution are also studied, and it is pointed out that the transition from sliding friction to static friction provides a dynamical correspondence to the occurrence of stable state.

Key words: dynamics of rigid body, linear approximation, dimensionless, fixed point, damped oscillation