Deep discussion about a mechanics problem of Chinese Physics Olympiad
Starting from a mechanics problem of Chinese Physics Olympiad,this paper delves into the motion of a slider on a smooth hemisphere under the influence of gravity.Beginning with a straightforward application of conservation laws to address the original query,this paper proceeds to derive the slider's dynamic equations through force analysis using Newtonian mechanics.Furthermore,an analysis is carried out from the perspectives of Lagrangian and Hamiltonian mechanics,as well as the weak field approximation of general relativity,deriving dy-namic equations consistent with those obtained via Newtonian mechanics.Numerical solutions are then employed to solve the dynamic equations,allowing for the visualization of the slider's trajectory.Finally,a comparison is made between the trajectory of the slider's motion on the smooth hemisphere under gravity and that on a vertical smooth conical surface.
conservation of angular momentumconservation of mechanical energyEuler-Lagrange equa-tionHamilton's canonical equationsweak field approximation of general relativity
万方数据
维普
