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A realistic treatment for numerical solution of equations of motion for systems involving coulomb friction requires three sets of dynamic equations: one for sticking, one for slipping, and one for transition from sticking to slipping. An alternative treatment of stick–slip motion is described, which involves only two sets of equations, one for sticking and the other for transition and slipping. The new approach uses a single equation that continuously relates frictional forces with normal forces for both the slipping and transition phases of motion. It turns out that this equation is also capable of approximating sticking as slipping at in nitesimally small speeds, but it is computationallymore ef cient to use two sets of equations. The new approach is computationally ef cient and is uni ed in the sense that when the equations of motion are cast into matrix form, the set of unknown variables is preserved during the various phases of motion (sticking, slipping, and transition), with only the last few rows of the aforementioned matrix having elements that change depending on the phase of motion. The equivalence of this new approach to the classical treatment of coulomb friction is established by comparisons of numerical results from several simulations, namely, the spin reversal of the rattleback, the effects of disturbances on a sleeping top, and the motion of a uniform sphere on a rough horizontal surface. It is shown that the same equations of motion describe the three systems for different choices of parameters.
Mitiguy et al. (Fri,) studied this question.