Dynamics of the Rolling Disk in the Presence of Dry Friction
Authors: Cédric Le Saux,
This research project is concerned
with the dynamics and numerical treatment of a rolling disk on a flat support.
The objective is to develop a numerical model which is able to simulate the
dynamics of a rolling disk taking into account various kinds of friction models: resistance
against sliding, pivoting and rolling. A mechanical model of a rolling disk is
presented in the framework of Non-smooth Dynamics and Convex Analysis.
Model of the rolling disk.
Nonsmooth dynamics provides an extended concept of classical
analytical mechanics with all its subdisciplines and modern extensions, such
as multibody dynamics and robotics, by allowing for set-valued constitutive
laws and discontinuities in the state variables as functions of time.
Set-valued constitutive laws provide a sound basis for switching on and off
various kinds of constraints in a most consistent way, where the switching
rules are embedded in the constitutive laws themselves.
analytical study, approximations are derived for the energy decay of the
system during the final stage of the motion for various kinds of frictional
dissipation models. Finally, the numerical and analytical results are
discussed and compared with experimental results available in literature.
See also the follow-up project:
Experimental and Theoretical Analysis of Spinning Objects with Frictional
Position of the center of mass
of the rolling disk.
Le Saux C.,
R. I., Glocker Ch.,
Dynamics of a Rolling Disk in the Presence of Dry Friction. Journal of
Nonlinear Science 15 (1), pp. 27–61, February 2005.
PDF (1403 kB)
Leine R. I., Le
Saux C., Glocker Ch.,
Friction Models for the Rolling Disk. Proc. 5th
EUROMECH Nonlinear Oscillations Conference, Eindhoven, August 7–12, 2005,
PDF (910 kB)