RollingDisk index
The rolling disk problem has many aspects which can be woven into the standard
range of teaching topics in applied maths.
- Numerical solution and graphics is easy. (NDSolve, etc.)
- Stability of equilibria for autonomous systems y'=f(y) is easy and
less trivial, i.e. more interesting, than in the standard "nonlinear pendulum" example.
(This is not to say that the "nonlinear pendulum" example should be omitted.)
The Jacobian matrix has the neat property that
J3=lambda J
and this allows a simple formula for the exponential matrix.
There is an interesting toy, Euler's disk (but I can't do anything useful associated with
the dissipation), which motivates study of the family of equilibria where the point of
contact moves in a circle and the centre of the disk is fixed.
- Energy conservation follows from our d.e.s (D) quite easily.
- For motions close to the horizontal, the neat d.e.
a'' = 1/a^3 - 1
arises and this has
- other physical applications (particle sliding in a cone, central orbits with constant attracting force)
- a closed form for the period
- a nice phase portrait
- There are more grown-up aspects to it, for possible use in advanced teaching,
associated with the fact that the system (D) is integrable.
- And the lecturers want to keep their brains in use even in moderately
low-level (2nd year) units.
Here is an item on the connections between
teaching and research circulated to UWA staff in 2006.
Teaching-related items
MATH2200, Mathematica materials
MATH2200 is
2nd year Applied Maths.
The unit is required as part of a Physics major or of an Applied Maths major.
Mathematica is used extensively.
The lecturing is shared between Maths and Physics.
Simon Tyler's code at Wolfram Demonstrations site:
http://demonstrations.wolfram.com/DiskRollingOnAHorizontalPlane/
- MATH2200 Labs (Rolling Disk in 2010);
MATH2200 Exams (See Q4 of the 2008 Exam).
-
Lecture handouts (used in 2008, 09, available on the web in 10 but a lot less in
lectures in 2010 but some material transfered to Labs in 2010)
MATH2235, 2006 Matlab materials
MATH2235 is a discontinued Eng. Maths unit. It had lots of the traditional o.d.e. and
linear algebra in it, including a little on the numerical solution of o.d.e..
Engineering students are Matlab users. In the unit replacing MATH2235 numerical solution
of o.d.e. has been removed, so the rolling disk example is a lot less appropriate than
it was in 2006.
- CAS bits from 2006
- Matlab:
- Maple (wasn't used in teaching, but was used in helping the
lecturer with his algebra, special function work, etc.)
- Mathematica (probably has more than just 2006)
- 2006 Exam paper
Solutions to 2006 Exam questions: several of the questions
being in the teaching paper:
scanned in solutions (links to pdf)
Publication effort, seminars
- Submitted, Oct 2009, Accepted May 2010
EMAC09
Eng. Maths and Applications Conference
- I have had a couple of earlier attempts at submitting teaching-related
papers, but seem to miss the criteria expected of the journals.
The miss seems to be by 'not a lot', and the referees say the
maths is OK (but are more often critical of the exposition
than not).
- Submitted, Mar 2009.
AJEE
Rejected, end Jun 2009. `Nothing wrong with the maths, but
the exposition isn't good enough' (and, perhaps it isn't close
enough to engineering).
(It was also criticised as being "too long", but here the problem was that the
editor gave me approval for it being longer than the guidelines but failed to
tell the referees.)
- Submitted, Sep 2006
http://www.tandf.co.uk/journals/authors/tmesauth.asp
tMESkeady.ps
tMESkeady.pdf
tMESkeady.tex
Referee's report Jan 07 (`nothing wrong with the maths, but
I don't like the exposition') give some hope that something might
get accepted, but a fair amount of re-writing (in directions GK didn't want
it taken) was requested.
Plots used in the paper include:
-
Seminar abstracts
seminar, 4th Sep 2006, at UWA
seminar, 13th Oct 2006, at RMIT
Paul Abbott presented the seminar at EMAC09.
- my tex files
The tex source is probably un-runnable by others as
it gets various bits of inputs from sundry places.
\input{../../lecTopMatter.tex}
../../lecTopMatter.tex
Miscellaneous bits
- Other Euler disk bits (i.e. involving dissipation)
There is nothing significant in my scribbles as they were just
oriented towards getting a few pictures into the lecture notes.
It was nice to end a lecture with both
the Euler disk and the lecturer stopping (on time) "in finite time".
- C and mex, for conical Legendre functions
The conical Legendre functions are in the gsl library.
The matlab mex work, *if* it ever gets done,
will be done in a subdirectory of NumSol
This file first created on Mon Oct 17 12:08:18 WST 2005
Validated Fri Jun 26, 2009, Mon May 10 2010
