iSoul In the beginning is reality

Motion Equations

The kinematic equations of motion have different forms depending on whether the motion is linear or angular (rotational) and whether space or time are 3D. They are given below and in a pdf here.

Parallel Equations of Motion

  Linear w/3D Space Linear w/3D Time Angular w/3D Space Angular w/3D Time
Position Linear length: s(t) Linear time: t(s) Angular length: θ(s) Angular time: φ(t)
Instantaneous Velocity/ Legerity Linear velocity

v = ds/dt = R/Q = S/T

vR = dr/dt, vT = ωR

Linear legerity

u = dt/ds = Q/R = T/S

uR = dw/ds, uT = ψQ

Angular velocity

ω = dθ/dt = dt/dφ

ω = vR/R = 2π/T

Angular legerity

ψ = dφ/ds = ds/dθ

ψ = uR/Q = 2π/S

Instantaneous Acceleration/ Expedience
Acceleration

a = dv/dt := 1/b

Expedience

b = du/ds := 1/a

Angular acceleration

α = dω/dt

Angular expedience

β = dψ/ds

Radial/Tangential Acceleration/ Expedience
Acceleration

aR = v2/R = v/Q

aT = αR

Expedience

bR = u2/Q = u/R

bT = βQ

Angular acceleration

aR = v2/R = ω2R

α = aT/R

Angular expedience

bR = ψ2Q = u2/Q

β = bT/Q

Uniform Rates v = 2πR/T u = 2πQ/S vT = ωR uT = ψQ
Radius Spatial radius

R = S/(2π) = vQ

Temporal radius

Q = T/(2π) = uR

Spatial radius

R = s/θ = v/ω = 1/ψ

Temporal radius

Q = t/φ = u/ψ = 1/ω

Circumference

Path Length

Circumference

S = 2πvQ = 2πR

Circumference

S = 2πQ/u = 2πR

Spatial path length

θ = s/R

Temporal path length

S = 2π/ψ

Period T = 2πR/v = 2πQ T = 2πuR = 2πQ T = 2π/ω φ = t/Q
Travel Length/Time s = vt = ωt R t = us = ψs/Q θ = s/(t R) = v/R ψ = t/s Q = u Q
Displacement s = s0 + vt t = (s ‒ s0)u θ = θ0 + ωt t = (θ θ0)/ω
First Equation of Space-Time v = v0 + at 1/u = (1/u0) + (t/b) ω = ω0 + αt t = (ωω0)/α
Second Equation of Space-Time s = s0 + v0t + ½at² t = (-u0/a) +

√[(u0/a)2 + 2(ss0)/a]

θ = θ0 + ω0t + ½αt2 φ = (-β/ψ0) +

√[(β/ψ0)2 + 2β(ss0)]

Third Equation of Space-Time = v0² + 2a(s s0) s = s0 + (v² ‒ v0²)/2a ω² = ω0² + 2α(θ θ0) θ = θ0 + (ω2ω02)/2α
Distimement s = (t ‒ t0)v t = t0 + us s = (φ φ0)/ψ φ = φ0 + ψs
First Equation of Time-Space 1/v = (1/v0) + (s/a) u = u0 + bs s =  (ψ ‒ ψ0)/β ψ = ψ0 + βs
Second Equation of Time-Space s = (-u0/b) +√[(u0/b)2 + 2(tt0)/b] t = t0 + u0s + ½bs² θ = (-α/ω0) +√[(α/ω0)2 + 2α(tt0)] φ = φ0 + ψ0t + ½βs2
Third Equation of Time-Space t = t0 + (u2u02)/2b u² = u0² + 2b(t t0) φ = φ0 + (ψ2ψ02)/2β ψ² = ψ0² + 2β(φ φ0)
Inertia/Facilia Mass (linear inertia): m Vass (linear facilia): n Rotational inertia: I = mr2 Rotational facilia: J = nt2
Momentum/ Fulmentum Momentum: p = mv Fulmentum: q = nu Angular momentum: L = Iω Angular fulmentum: Λ = Jψ
Kinetic Energy/ Invertegy Kinetic Energy: E = ½mv2 Kinetic invertegy: V = ½nu2 Rotational KE: ½2 Rotational KE: ½2
Force/Rush Force: F = ma Rush: Γ = nb Torque: τ = Iα Strophence: σ = Jβ
Work/Invork Linear work: W = Fs Linear invork: V = Γ t Rotational work: W = τθ Rotational invork: V = σφ
Power/Exertion Linear power: Fv Linear exertion: Γu Rotational power: τω Rotational exertion: σψ