  In the conceptual framework of phase ordering after temperature quenches
below transition, we consider the underdamped Bales-Gooding-type 'momentum
conserving' dynamics of a 2D martensitic structural transition from a
square-to-rectangle unit cell. The one-component or $N_{\rm OP} =1$ order
parameter is one of the physical strains, and the Landau free energy has a
triple well, describing a first-order transition. We numerically study the
evolution of the strain-strain correlation, and find that it exhibits dynamical
scaling, with a coarsening length $L(t) \sim t^{\alpha}$. We find at
intermediate and long times that the coarsening exponent sequentially takes on
respective values close to $\alpha=2/3$ and $\alpha=1/2$. For deep quenches,
the coarsening can be arrested at long times, with $\alpha \simeq 0$. These
exponents are also found in 3D. To understand such behaviour, we insert a
dynamical-scaling ansatz into the correlation function dynamics to give, at a
dominant scaled separation, a nonlinear kinetics of the curvature $g (t) \equiv
1/ L(t)$. The curvature solutions have time windows of power-law decays $g \sim
1/t^\alpha$, with exponent values $\alpha$ matching simulations, and manifestly
independent of spatial dimension. Applying this curvature-kinetics method to
mass-conserving Cahn-Hilliard dynamics for a double-well Landau potential in a
scalar $N_{\rm OP}=1$ order parameter yields exponents $\alpha = 1/4$ and $1/3$
for intermediate and long times. For vector order parameters with $N_{\rm OP}
\geq 2$, the exponents are $\alpha = 1/4$ only, consistent with previous work.
The curvature kinetics method could be useful in extracting coarsening
exponents for other phase-ordering dynamics.
