  We obtain the dynamics in number and phase difference, for Bose condensates
that tunnel between two wells of a double-well atomic trap, using the
(nonlinear) Gross-Pitaevskii equation.The dynamical equations are of the
canonical form for the two conjugate variables, and the Hamiltonian corresponds
to that of a momentum-shortened pendulum, supporting a richer set of tunneling
oscillation modes than for a superconductor Josephson junction, that has a
fixed-length pendulum as a mechanical model. Novel modes include "inverted
pendulum" oscillations with an average angle of \pi; and oscillations about a
self-maintained population imbalance that we term "macroscopic quantum
self-trapping". Other systems with this phase-number nonlinear dynamics include
twocomponent (interconverting) condensates in a single harmonic trap, and
He^{3}B superfluids in two containers connected by micropores.
