  We present an analytical description of the tunneling dynamics between two
coupled Bose-Einstein condensates in the Josephson regime. The model relies on
the classical analogy with a rigid pendulum and focuses on two dynamical modes
of this system: Josephson oscillations and Macroscopic Quantum Self-Trapping.
The analogy is extended to include an energy difference between the two
superfluids caused by an asymmetry in the trapping potential. The model is
compatible with the mean-field predictions of the two-mode Bose-Hubbard model.
It gives new insights on the mean-field model by involving experimentally
measurable parameters with reduced correlations. For agreement with recent
experimental observations, we establish heuristic formulas including a
dissipation. We conclude with a convincing application of the model to several
sets of experimental results.
