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 = (ω ‒ ω0)/α Second Equation of Space-Time s = s0 + v0t + ½at² t = (-u0/a) + √[(u0/a)2 + 2(s ‒ s0)/a] θ = θ0 + ω0t + ½αt2 φ = (-β/ψ0) + √[(β/ψ0)2 + 2β(s ‒ s0)] Third Equation of Space-Time v² = v0² + 2a(s – s0) s = s0 + (v² ‒ v0²)/2a ω² = ω0² + 2α(θ – θ0) θ = θ0 + (ω2 ‒ ω02)/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(t ‒ t0)/b] t = t0 + u0s + ½bs² θ = (-α/ω0) +√[(α/ω0)2 + 2α(t ‒ t0)] φ = φ0 + ψ0t + ½βs2 Third Equation of Time-Space t = t0 + (u2 ‒ u02)/2b u² = u0² + 2b(t – t0) φ = φ0 + (ψ2 ‒ ψ02)/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: ½Iω2 Rotational KE: ½Jψ2 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