IMPACT MODEL RESOLUTION ON PAINLEVE’S PARADOX

Painlevé‘s paradox is one of the basic difficulties for solving LCP of dynamic systems subjected to unilateral constraints. A bi-nonlinear parameterized impact model, consistent with dynamic principles and experimental results, is established on the localized and quasi-static impact model theory. Numerical simulations are carried out on the dynamic motion of Painlevé‘s example. The results confirm ““““impact without collision““““ in the inconsistent states of the system. A ““““critical normal force““““ which brings an important effect on the future movement of the system in the indeterminate states is found. After the motion pattern for the impact process is obtained from numerical results, a rule of the velocity‘s jump that incorporates the tangential impact process is deduced by using an approximate impulse theory and the coefficient of restitution defined by Stronge. The results of the jump rule are quite precise if the system rigidity is big enough.

Impact model resolution on Painlevé's paradox

Painlevé's paradox is one of the basic difficulties for solving LCP of dynamic systems subjected to unilateral constraints. A bi-nonlinear parameterized impact model, consistent with dynamic principles and experimental results, is established on the localized and quasi-static impact model theory. Numerical simulations are carried out on the dynamic motion of Painlevé's example. The results confirm “impact without collision” in the inconsistent states of the system. A “ritical normal force” which brings an important effect on the future movement of the system in the indeterminate states is found. After the motion pattern for the impact process is obtained from numerical, results, a rule of the velocity's jump that incorporates the tangential impact process is deduced by using an approximate impulse theory and the coefficient of restitution defined by Stronge. The results of the jump rule are quite precise if the system rigidity is big enough. The project supported by the National Natural Science Foundation of China (10272002), Doctoral Foundation of Educational Ministry of China (20020001032) and the foundation (024132009203235)