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.

Parallel Equations of Motion

  Linear w/3D Length Space Linear w/3D Duration Space
Angular w/3D Length Space Angular w/3D Duration Space
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

Radius | Stance | Time
Stantial radius

r = S/(2π) = qv

Temporal radius

q = T/(2π) = ru

Stantial radius

r = s/θ = v/ω = 1/ψ

Temporal radius

q = t/φ = u/ψ = 1/ω

Velocity | Legerity Linear/Tangential velocity

vT = ds/dt = rω = r/q = S/T

Linear/Tangential legerity

uT = dt/ds = qψ = q/r = T/S

Angular velocity

ω = dθ/dt = dt/dφ = v/r = 1/q

Angular legerity

ψ = dφ/ds = ds/dθ = u/q = 1/r

Acceleration | Expedience Radial acceleration

aR = v2/r = rω2 = v/q = r/q²

Radial expedience

bR = u2/q = 2 = u/r = q/r²

Angular acceleration

α = dω/dt = aT/r

Angular expedience

β = dψ/ds = bT/q

Tangential acceleration

aT = dvT/dt = rα

Tangential expedience

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 Reserve Kinetic energy: KSE = ½mv2 Kinetic reserve: KTE = ½nu2 Rotational KSE: ½Iω2 Rotational KTE: ½Jψ2
Newton’s Second Law of Motion Force: F = ma Rush: Y = nb Torque: τ = Iα Strophence: σ = Jβ
Work | Surge Linear work: W = Fs Linear surge: V = Yt Rotational work: W = τθ Rotational surge: V = σφ
Power | Alacrity Linear power: P = Fv Linear alacrity: Q = Yu Rotational power: P = τω Rotational alacrity: Q = σψ