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 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 | Base | Time Basal radius r = S/(2π) = qv Temporal radius q = T/(2π) = ru Basal 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 = qψ2 = 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 ∙ (s – s0) u² = u0² + 2b ∙ (t – t0) ω² = ω0² + 2α ∙ (θ – θ0) 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: 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 = F ∙ s Linear surge: V = Y ∙ t Rotational work: W = τ ∙ θ Rotational surge: V = σ ∙ φ Power | Alacrity Linear power: P = F ∙ v Linear alacrity: Q = Y ∙ u Rotational power: P = τ ∙ ω Rotational alacrity: Q = σ ∙ ψ