Proportional selective modification of dynamical systems by "exterior dissipation"

I will introduce a technique for adding dissipation or otherwise modifying dynamical systems to selectively change any number of conserved quantities, while only reducing the total number of conserved quantities by one. I will first present a naïve approach to a simple example, a textbook problem of a specially damped rotor often used to explain the famous failure of the Explorer 1 satellite. Then (in joint work with M. Aureli), we generalize the approach to any number of dimensions and conserved quantities. The resulting dynamics drives the modified system to a nontrivial state of the original system, such as a limit cycle.