  We present a theory of geodynamics in a spacetime crystal based on an event
wavepacket constructed from the Floquet-Bloch waves, which not only involve a
scalar dispersion function but also a Berry curvature tensor in the phase space
manifold of spacetime and the reciprocal quasi energy-momentum. In the presence
of structural deformation, this theory is naturally extended into a covariant
form with the introduction of a lattice connection constructed out of the
gradients of the local lattice vectors. The geodesic equation for a free
particle involves not only the lattice connection but also higher-order
corrections from spacetime inhomogeneity of Berry curvatures and quasi
energy-momentum dispersion.
