I'm working with a kinetic energy KERS (Kinetic Energy Recovery and Storage) system that use a flywheel coupled via an IVT (Infinitely Variable Transmission) to a vehicle. The vehicle load is Ib and Lb is known at the driveshaft. Considering only the inertial loads (I.E. ignoring all friction or drag) I basically have a flywheel of Inertia Ia rotating initially at ωao, thus having an initial momentum of La=Ia*ωa. The IVT has a ratio range of infinity:10, or 1/r = 0:0.1 = n. Initially then there is no output of the IVT to the vehicle. We then vary n form 0 to 0.1 over a period t. I have tried multiple methods to find ωa(n) and know that torque on the IVT housing must be used to determine total momentum. I've tried simultaneously solving the mometum and energy balance equations but not been successful arriving at a solution that satisfies conservation of energy and momentum. Any help will be greatly appreciated.