# Chapter seven comments

## Leo Mariani

This chapter is the most difficult one that we have studied so far. The introduction to configuration space by way of the goniometer is an excellent one. We finally start to assign coordinates to quantities and study dimensions as specific coordinates. I started to get a little lost when you started talking about the project of Kocak and Bisshopp and their two pendulums. What is the location of the orbits of the pendulums on the torus in the hypersphere? Are the orbits perpendicular to each other with one pendulum representing longitude and the other pendulum latitude? The organization of chapters is slightly vague in my opinion. What is the connection between differential topology and wave fronts and focal curves in the plane. What exactly are cusps defined as? Are they simply any points where singularity occurs? I am finding it very difficult to understand the evolute of the ellipse. Is it supposed to be the collection of cusps where the ellipse is a endlessly propagating, dynamic, wave system? I have no idea what the relationship of this is to tyhe light caustic. Overall, I am befuddled by this chapter, and I hope that some in class discussion will enlighten me somewhat.