Rates of motion in time and distance domains

The rates of motion for translational (linear) and rotational (angular) motion in the time domain and the distance domain are as follows:

Time Domain

Variable

Translational Motion

Rotational Motion

Location

x

θ

Velocity

v = dx/dt

ω = /dt

Acceleration

a = dv/dt

α = dω/dt

Distance Domain

Variable

Translational MotionRotational Motion

Chronation

z

ϕ

Lenticity

w = dz/ds

ψ = /ds

Relentment

b = dw/ds

β = /ds