Painlevé paradox
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Painlevé paradox is a well known example by Paul Painlevé in rigid-body dynamics which showed that rigid-body dynamics with contact and friction is inconsistent. This is due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law, especially when dealing with large coefficients of friction.[1]
Modeling rigid bodies and friction greatly simplifies such applications as animation, robotics and bio-mechanics, it is only an approximation to a full elastic model requiring complex systems of partial differential equations.
The paradox was resolved in the 1990s by David E. Stewart.[2]
[edit] References
- ^ Paul Painlevé (1895). C. R. Acad. Sci. (Paris) 121: 112-115.
- ^ Stewart, David E. (2000). "Rigid-Body Dynamics with Friction and Impact". SIAM 42 (1): 3-39. doi:. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SIREAD000042000001000003000001&idtype=cvips&gifs=yes.
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