This paper proposes a mechanical solution to save fuel by shutting down an internal combustion engine whenever it is unnecessary for propulsion, e.g., when a vehicle is waiting for traffic lights. The engine and vehicle are restarted using the energy that is stored in a flywheel. Two additional clutches are needed to enable appropriate power flow from the flywheel to the engine and vehicle. This complicates the powertrain dynamics in that the number of degrees of freedom changes due to clutch operations. Therefore, a hybrid control strategy, which is treated as a top-level controller, is introduced to deal with this finite-state mechanical system. At the lower level, the engine and clutches are controlled in a coordinated manner such that the vehicle is launched according to the driver's demands. Using a comprehensive powertrain simulation package, the proposed controller is evaluated numerically.