today in my physics course we were using jacobians to transform coordinate systems. This made me wonder if there was a way of deriving an optimal coordinate system to use for a given problem. -optimal meaning most simplified equation of a surface or bounds of a constraint (ex. cylindrical coordinates for modeling a solenoid, polar for pendulum motion) I know that usually we just look at a problem and use what we think will simplify things the most, but I think it would be useful in complex problems to derive it. Lagrange's method in mechanics uses generalized coordinates, so maybe I could use it to solve for them somehow? anyone have any idea about this?