  We analyze how the orbital support of the inner bar in a double-barred galaxy
(nested bars) depends on the angular velocity (i.e. pattern speed) of this bar.
We study orbits in seven models of double bars using the method of invariant
loops. The range of pattern speed is covered exhaustively. We find that not all
pattern speeds are allowed when the inner bar rotates in the same direction as
the outer bar. Below a certain minimum pattern speed orbital support for the
inner bar abruptly disappears, while at high values of this speed the orbits
indicate an increasingly round bar that looks more like a twist in the nuclear
isophotes than a dynamically independent component. For values between these
two extremes, orbits supporting the inner bar extend further out as the bar's
pattern speed decreases, their corresponding loops become more eccentric,
pulsate more, and their rotation becomes increasingly non-uniform, as they
speed up and slow down in their motion. Lower pattern speeds also lead to a
less coherent bar, as the pulsation and acceleration increasingly varies among
the loops supporting the inner bar. The morphologies of fast and slow inner
bars expected from the orbital structure studied here are recently recovered
observationally by decomposition of double barred galaxies. Our findings allow
us to link the observed morphology to the dynamics of the inner bar.
