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The Bogoliubov approximation and the Gross-Pitaevskii equation characterizethe effect of repulsive interactions on a dilute ideal Bose-Einstein gas in aspherical harmonic trap. For large $N$, the interactions expand the condensaterelative to an ideal Bose gas; both the speed of sound and critical angularvelocity $\Omega_{c1}$ for creation of a quantized vortex depend crucially onthe interparticle repulsion through the coherence length $\xi$.

DILUTE BOSE-EINSTEIN CONDENSATE IN A TRAP: CHARACTERISTIC LENGTHS AND CRITICAL VELOCITIES