iSoul In the beginning is reality.

Motion Equations

Equations for circular/harmonic and spiral/helical motion in length and duration space is given in a pdf here. The kinematic equations below have different forms depending on whether the motion is linear or angular (rotational) and whether length and duration are vector (3D) or scalar (1D). They are also given in a pdf here. Circular/harmonic motion equations are here.

Parallel Equations of Motion

  Linear w/3D Space Linear w/3D Time
Angular w/3D Space Angular w/3D Time
Length/Location | Duration/Chronation Linear length: s

Linear location: s

Linear duration: t

Linear chronation: t

Length space arc: s

Angular length: θ = s/r

Duration space arc: t

Angular duration: φ = t/q

Stance | Time
Spatial radius (stance)

r = S/(2π) = qv

Temporal radius

q = T/(2π) = ru

Spatial radius (stance)

r = s/θ = v/ω = 1/ψ

Temporal radius

q = t/φ = u/ψ = 1/ω

Velocity | Lenticity Linear/Tangential velocity

vT = ds/dt = rω = r/q = S/T

Linear/Tangential lenticity

uT = dt/ds = qψ = q/r = T/S

Angular velocity

ω = dθ/dt = dt/dφ = v/r = 1/q

Angular lenticity

ψ = dφ/ds = ds/dθ = u/q = 1/r

Acceleration | Retardation Radial acceleration

aR = v2/r = rω2 = v/q = r/q²

Radial retardation

bR = u2/q = 2 = u/r = q/r²

Angular acceleration

α = dω/dt = aT/r

Angular retardation

β = dψ/ds = bT/q

Tangential acceleration

aT = dvT/dt = rα

Tangential retardation

bT = duT/ds = qβ

Circumference | Period S = 2πr = 2πvq T = 2πq = 2πur S = 2π/ψ T = 2π/ω
Revolutions | Repetitions

Frequency | Circuncy.

N = θ/(2π) Z = φ/(2π) f = ω/(2π) = 1/T h = ψ/(2π) = 1/S
Displacement | Dischronment s = s0 + vt t = t0 + ux θ = θ0 + ωt φ = φ0 + ψs
First Equation of Motion v = v0 + aTt u = u0 + bTs ω = ω0 + αt ψ = ψ0 + βs
Second Equation of Motion s = s0 + v0t + ½aTt² t = t0 + u0s + ½bTs² θ = θ0 + ω0t + ½αt2 φ = φ0 + ψ0t + ½βs2
Third Equation of Motion v² = v0² + 2a ∙ (ss0) u² = u0² + 2b ∙ (tt0) ω² = ω0² + 2α ∙ (θθ0) ψ² = ψ0² + 2β ∙ (φφ0)
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: Γ = Jψ
Kinetic Energy and Lethargy Kinetic energy:  KE = ½mv2 Kinetic lethargy: KL = ½nu2 Rotational  RE: ½Iω2 Rotational RL: ½Jψ2
Newton’s Second Law of Motion Force: F = ma Rush: Y = nb Torque: τ = Iα Strophence: σ = Jβ
Work | Repose Linear work: W = Fs Linear repose: V = Yt Rotational work: W = τθ Rotational repose: V = σφ
Power | Alacrity Linear power: P = Fv Linear alacrity: Q = Yu Rotational power: P = τω Rotational alacrity: Q = σψ