The tools used for assessment of rotor angle stability should be able to estimate the domain of attraction and the ensuing control laws which would aid in enhancing it. The widely used energy function formulations have limitations in being extended for lossy N-machines owing to the presence of transfer conductances obtained due to the modeling approaches used in transient stability studies. This problem is akin to the N-body problem in celestial mechanics, for which, solutions exist, but finding analytical solutions fail beyond the two body case. The dynamics of the N-body system motivates the authors to assert that integrability and synchronization can exist independently. The major contribution of the paper is the application of the Watanabe-Strotgatz theory for oscillators to the N-machine system and prove that integrability of the system can be achieved only at certain extremes of the transfer conductances, but is generically, not achievable.