  We present measurements of decay matrix elements for hadronic transitions of
the form Upsilon(nS) -> pi pi Upsilon(mS) where (n, m) = (3, 1), (2, 1), and
(3, 2). We reconstruct charged and neutral pion modes with the final state
Upsilon decaying to either mu+mu- or e+e-. Dalitz plot distributions for the
twelve decay modes are fit individually as well as jointly assuming isospin
symmetry, thereby measuring the matrix elements of the decay amplitude. We
observe and account for the anomaly previously noted in the di-pion invariant
mass distribution for the Upsilon(3S) -> pi pi Upsilon(1S) transition and
obtain good descriptions of the dynamics of the decay using the most general
decay amplitude allowed by partial conservation of the axial-vector current
(PCAC) considerations. The fits further indicate that the Upsilon(2S) -> pi pi
Upsilon(1S) and Upsilon(3S) -> pi pi Upsilon(2S) transitions also show the
presence of terms in the decay amplitude that were previously ignored, although
at a relatively suppressed level.
