By Sköldstam 1975- Markus
Research of the section area of heavy symmetric most sensible (ISBN 9173739944)
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Additional resources for Analysis of the phase space, asymptotic behavior and stability for heavy symmetric top and tippe top
5 Karnopp Friction Model In 1985, Dean Karnopp proposed a friction model to overcome the problems with zero velocity detection and to avoid switching between different state equations for sticking and sliding . The friction Karnopp model considers a small velocity window near zero speed. Outside the velocity window (slip region), the friction force is an arbitrary function of velocity. 1 Friction Modeling 31 force required to keep zero acceleration. The system enters the sticking region when the speed is in the velocity window and the net external force is less than or equal to the limiting static friction force.
The axial, torsional, and lateral vibrations of the discrete system are coupled through these interaction forces and torques, see . 2 Distributed Parameter Models To the best of the author’s knowledge, the very first model of drilling vibrations was developed in the 1960s at the Shell Development Company, by Bailey  and Finnie . They proposed a wave equation model to analytically treat the longitudinal and torsional drilling vibrations. Due to the accuracy of this modeling approach in reproducing the drilling behavior, regarding its distributed nature, it constitutes the basis of several recent contributions on drilling analysis and control.
It includes the classical Dahl friction model, the LuGre model, and the Bliman-Sorine model. An analysis on the effects of friction, particularly the stick-slip phenomenon, in control systems is also presented. The aforementioned models of friction and some other classical ones, such as the Leuven integrated friction model can be found in . Furthermore, some methods for friction compensation are therein reviewed. In , a comparison of the Bliman-Sorine and the LuGre model is presented.
Analysis of the phase space, asymptotic behavior and stability for heavy symmetric top and tippe top by Sköldstam 1975- Markus