How to simulate a ponytail, part 2

Building on a previous article, more aspects of how to simulate a ponytail in a computer or video game are discussed. In part one, it was decided to do the derivation for two constrained bodies first, to keep things manageable, and then later generalize it to the longer chain of bodies that make up the ponytail. At the end of part one, equations for the linear and angular accelerations of the simple 2-body system when they were affected by the contract force, f(c), were written out. Further, it was decided that this constraint equation would be the one to satisfy at all times during the simulation. If this equation could be satisfied, then the situation started with the position and velocity constraint satisfied, there would be left a constrained rigid body simulator. How to work with these equations is detailed.