Bernard Brogliato:
Impact mechanics in multibody systems.
This talk will focus on the modelling of impact phenomena between rigid
bodies (or systems of rigid bodies):
1) single impacts without and with friction (algebraic models with
kinematic restitution coefficients, DarbouxKeller's approach and the
energetic coefficient of restitution)
2) multiple impacts without and with friction (a multiple impact occurs
if several impacts occur at the same time on a system).
The problem of multiple impacts is still an open issue in the realm of
impact mechanics. We will try to introduce the basics of multiple impact
modeling, in particular the fundamental reasons why multiple impacts are
not a direct extension of single impacts, in the sense that the
dissipation of the energy at the contact points is no longer sufficient
to get realistic models: one has to incorporate also the energy
dispersion that is mainly due to the wave propagation in the system. The
classical example of chains of balls will serve as an illustration,
which is worth studying in view of a better understanding of "simple"
granular systems. This is also an opportunity to realize that the
classical "textbooks" solution concerning the Newton's cradle, is quite
far from the problem's real complexity.
Lecture Slides
References:

Z. Zhao, C. Liu, B. Brogliato, 2009 ``Planar dynamics of a rigid body
system with frictional impacts. II. Qualitative analysis and numerical
simulations'', Proceedings of the Royal Society A, Mathematical,
Physical and Engineering Sciences, vol.465, no 2107, pp. 22672292, July.

C. Liu, Z. Zhao, B. Brogliato, 2009 ``Frictionless multiple impacts in
multibody systems: Part II. Numerical algorithm and simulation
results'', Proceedings of the Royal Society A, Mathematical, Physical
and Engineering Sciences, vol.465, no 2101, pp.123, January.

C. Liu, Z. Zhao, B. Brogliato, 2008 ``Frictionless multiple impacts in
multibody systems: Part I. Theoretical framework'', Proceedings of the
Royal Society A, Mathematical, Physical and Engineering Sciences,
vol.464, no 2100, pp.31933211, December.
The research reports corresponding to these papers are available
here and
here .