We calculate the L=0 ground and excited state energies for the rare gas trimers He-3, Ne-3, and Ar-3. An adiabatic representation is adopted to solve the nuclear Schrodinger equation, in which the Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B splines. We compare results obtained in a strict adiabatic approximation with nonperturbative coupled-adiabatic-channel calculations. Structural properties such as the pair and angle distributions are monitored as functions of the hyper-radius. These structural studies pinpoint the locus of configurational changes that occur as the trimer fragments into a diatom plus an atom. Analysis of the angular channel functions and their associated radial components permits an approximate classification of the vibrational spectrum.