iSoul In the beginning is reality

Parallel equations of motion

Expanding on the previous post here, this is a summary of the equations of motion for space-time and time-space. See also the Time-space Glossary option above.

r = displacement magnitude, t = time magnitude, v = velocity, v0 = initial velocity, a = acceleration, = allegrity, 0 = initial allegrity, b = modulation

Space-time (3+1) Time-space (1+3)
Assumption da / dt = 0 db / dr = 0
da / dr = 0 db / dt = 0
First equation of motion dv / dt = a d / dr = b
v = v0 + at v = v0 + br
Second equation of motion dr / dt = v = 1/ dt / dr = = 1/v
r = r0 + v0t + ½at² t = t0 + ℓ0r + ½br²
Third equation of motion dv / dr = a/v = aℓ d / dt = b/ = bv
= v0² + 2a(rr0) ℓ² = 0² + 2b(tt0)
2a = (v0²) / (rr0) 2b = (ℓ²0²) / (tt0)
Relation dv / d = a/bv = aℓ/b d / dv = b/aℓ = bv/a

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