Analytical Solutions for the Dynamics of Planetary Nebulae with and without Common Envelope Evolution

We present new analytical solutions for the dynamics of planetary nebulae. These equations consider the temporal variation of the mechanical luminosity as well as the common envelope evolution scenario. By comparing a database of nebulae with these solutions, a large portion of planetary nebulae can be better explained by the common envelope evolution scenario, especially the fast and slow ones. Single AGB stellar models can only reproduce nebulae with expansion velocities between 20 and 30 km/s.