Contact information
| Instructor: |
Dr. David Stewart |
| Phone: |
335-3832 |
| Email: |
dstewart at math
dot uiowa dot edu |
| WWW URL: |
http://www.math.uiowa.edu/~dstewart/ |
| Office hours: |
MW 1:30-2:30pm; Tu
10:30-11:30am |
| Class times: |
11:30-12:20am MWF |
| Class location: |
219
JH |
You can see me outside the office hours provided it is mutually
convenient.
This course will use Blackboard; go to http://bb6.uiowa.edu/ and log
in with your HawkID and
password.
Contact and impact phenomena where solid bodies make contact occur
all around us, and have been studied scientifically at least since
the time of Newton. They also have many, many applications. Here is
a sample:
- Robotics (get a robot to grab a cup, and put it on a table)
- Biomechanics (walking, running, jumping)
- Manufacturing (orienting parts, assembly)
- Computer graphics (physically-based animation, computer games)
However, the usual tools we have for modelling physical systems
(ordinary
and partial differential equations) need to be extended to deal with
contact phenomena.
We will focus mostly on rigid-body dynamics and ordinary
differential
equations. Later we will look at elastic-bodies in impact which means
partial differential equations. In both cases we can model the
mechanical
system with variational inequalities and complementarity
problems. How these are combined with differential equations to
describe
dynamic behavior will be a big part of this course.
Not only will we talk about continuous models, but we will discuss
discrete approximations that can be implemented to simulate mechanical
systems with impacts.
- Basic mechanics of particles and rigid-body systems.
- Signorini contact conditions.
- Coulomb friction laws.
- Impact laws for rigid-body dynamics (Newton, Poisson, others).
- Static contact problems (finite-dimensional) for rigid-bodies.
- Complementarity problems and their solution (Lemke's algorithm).
- Application of complementarity problems to rigid-body dynamics.
- Painlevé's paradox and its resolution.
- Simulation of rigid-body dynamics.
- Limits of rigid-body theories (Chatterjee's thought experiment,
Hurmuzlu's
actual experiment).
- Elastic body contact problems -- static, quasistatic, and
dynamic.
- Ill-posedness of Coulomb friction law.
- Current knowledge and open questions.
I don't have a textbook, but there are some books that would be useful
as references:
- Inequalities in Mechanics and Physics, by G. Duvaut
and J.L. Lions.
- Impact Mechanics, by W. Stronge.
- Nonsmooth Impact Mechanics: models, dynamics, and control,
by B. Brogliato.
Pre-requisites
Necessary: Ordinary
differential equations
Helpful: Some numerical
analysis/methods, some partial differential equations
Assessment will be through some homework and some project work.
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David Stewart
2004-10-04