Temporo-spatial physics parallels spatio-temporal physics. Here is a derivation of the corresponding equations of motion, paralleling the exposition at the Physics Hypertextbook.
The one-dimensional equations of motion for constant relentation:
Let t = time, t0 = initial time, r = displacement, u = lenticity, u0 = initial lenticity, b = relentation.
First equation of motion
b = du / dr
du = b dr
∫ du from u0 to u = ∫ b dr from 0 to r
u – u0 = br
u = u0 + br
Second equation of motion
u = dt / dr
dt = u dr = (u0 + br) dr
∫ dt from t0 to t = ∫ (u0 + br) dr from 0 to r
t – t0 = u0r + ½br²
t = t0 + u0r + ½br²
Third equation of motion
du / dt = (du / dt) (dr / dr) = (du / dr) (dr / dt) = b / u
u du = b dt
∫ u du from u0 to u = ∫ b dt from t0 to t
½(u² – u0²) = b(t – t0)
u² = u0² + 2b(t – t0)
Since displacement is in the denominator and time is in the numerator of lenticity and relentation, these equations may be generalized to three dimensions of time.