  A description of the martensitic transformations between the $\alpha$,
$\beta$ and $\omega$ phases of titanium that includes nucleation and growth
requires an accurate classical potential. Optimization of the parameters of a
modified embedded atom potential to a database of density-functional
calculations yields an accurate and transferable potential as verified by
comparison to experimental and density functional data for phonons, surface and
stacking fault energies and energy barriers for homogeneous martensitic
transformations. Molecular dynamics simulations map out the
pressure-temperature phase diagram of titanium. For this potential the
martensitic phase transformation between $\alpha$ and $\beta$ appears at
ambient pressure and 1200 K, between $\alpha$ and $\omega$ at ambient
conditions, between $\beta$ and $\omega$ at 1200 K and pressures above 8 GPa,
and the triple point occurs at 8GPa and 1200 K. Molecular dynamics explorations
of the dynamics of the martensitic $\alpha-\omega$ transformation show a
fast-moving interface with a low interfacial energy of 30 meV/\AA$^2$. The
potential is applicable to the study of defects and phase transformations of
Ti.
