Ridged chain

It is one animation of the task "Pendulum-chain" for my article "Games with Chain".

See please the Russian variant of the article. and Mathcad 15 sheet in attach!

But I have some question:

1. Do you know some descriptions and solutions of this problem?

2. Can you help me to use not a X-Y plot but a polar plot for the solution and for an illustrations?

3. Can we think about a symbolic solution?

4. Can we have better initial conditions for the not crazy numerical solution and for more nice moving of the Pendulum-chain?

Thank you!