This assignment asks you to:
(1) develop a model of a physical system in the form of a system of ODEs,
(2) determine if a certain kind of behavior (i.e. solution) occurs in the system by analytical and/or numerical means.
In a world far from this one, inhabitants engage in a sport called
"baton twirling". 
The baton, a
rigid stick a little shorter than your arm and with a knob at each end
is thrown repeatedly into the air with substantial angular velocity and caught
again. Moreover, it is reported that a twirling baton can be made to rotate
round and round an extended arm or leg, somehow adhering
to the limb rather than falling! Is this possible??
I am asking you to perform a mathematical analysis of this problem, and attempt to answer
the question definitively and quantitatively.
(i) An initial discussion of the problem today in class. Draw some sketches. Decide what the variables are, etc.
(ii) By consulting appropriate textbooks in the library or otherwise, determine the generic equations of motion for a rigid body under the simplifying circumstances (planar motion, symmetry of body) of our problem. Submit a description of these equations as part of HW#7, due Friday 11/6.
(iii) Develop an ODE model of the baton motion, and submit a preliminary description of your model by Friday, 11/20.
(iv) Use analytical and/or numerical means to explore the solutions of your system of ODEs, determining whether or not the kind of behavior described above can occur (in your model). Submit a carefully prepared report of your work and your findings by Friday, Dec 11. Your report should include graphical representations of your solutions, and perhaps even animations of the baton in motion.
Comment: The trickiest part of the modelling, in my opinion, concerns the force on the baton at its point of contact with the twirler's arm. Note that it has tangential as well as normal components. A sensible working hypothesis is that there is no slip. This hypothesis might turn out to be inconsistent: if so, at that time it would be necessary to include more information from physics: a model of the relationship between frictional force, normal force, and sliding velocity.