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Motion Equations

The motion equations for classical physics below are also in a pdf here. Circular/harmonic motion equations are in a pdf here. Motion equations for relativity are in a pdf here.

Parallel Equations of Motion
RA Gillmann, 2020-02-06 Displacement + Time Dischronment + Stance Spatial Angles + Time Temporal Angles + Stance
Stance/Distance | Time/Distime Displacement: s

Time | duration: t

Dischronment: t

Stance | length: s

Spatial angle: θ = s/r

Temporal arc: t

Temporal angle: φ = t/q

Spatial arc: s

Radius | Period Spatial radius

r = S/(2π) = qv

Temporal radius

q = T/(2π) = ru

Angular velocity

ω = φ/t = κ/u = 2πf = 2π/T = dθ/dt = dt/dφ = v/r = 1/q

Wavenumber (angular lenticity)

κ = θ/s = ω/v = 2πh = 2π/λ = dθ/ds = ds/dφ = u/q = 1/r

Velocity | Lenticity | Wavenumber Cross/Tangential velocity

v = ds/dt = r×ω = r/q = S/T

Cross/Tangential lenticity

u = dt/ds = q×κ = q/r = T/S

Acceleration | Retardation Radial acceleration
a = v2/r =2 = v/q = r/q²
Radial retardation
b = u2/q =2 = u/r = q/r²
Angular acceleration
α = dω/dt = aT/r
Angular retardation
β = dκ/ds = bT/q
Tangential acceleration
a = ω×v = Tdv/dt = rα
Tangential retardation
b = Tdu/ds = qβ
Wavelength | Period λ = S = 2πr = 2πvq T = 2πq = 2πur λ = S = 2π/κ = 1/h T = 2π/ω = 1/f
Revolutions | Repetitions
Frequency | Circuncy
Revolutions

N = θ/(2π)

Repetitions

Z = φ/(2π)

Temporal frequency
f = ω/(2π) = 1/T
Spatial frequency (circuncy)
h = κ/(2π) = 1/λ
Displacement | Dischronment s = s0 + vt t = t0 + ux θ = θ0 + ωt φ = φ0 + κs
First Equation of Motion v = v0 + at u = u0 + bs ω = ω0 + αt κ = κ0 + βs
Second Equation of Motion s = s0 + v0t + ½at² t = t0 + u0s + ½bs² θ = θ0 + ω0t + ½αt2 φ = φ0 + κ0t + ½βs2
Third Equation of Motion v² = v0² + 2a∙(s s0) u² = u0² + 2b∙(t t0) ω² = ω0² + 2α∙(θ θ0) κ² = κ0² + 2β∙(φ φ0)
Inertia | Facilia Mass (linear inertia): m = 1/n Etherance (linear facilia): n = 1/m Angular inertia: I = mr2 Angular facilia: J = nq2
Momentum | Fulmentum Momentum: p = mv Fulmentum: q = nu Angular momentum: L = Iω Angular fulmentum: Γ = Jκ
Kinetic Energy and Lethargy Kinetic energy: EK = ½mv2 Kinetic lethargy: LK = ½nu2 Angular energy EA = ½Iω2 Angular lethargy LA = ½Jκ2
Newton’s Second Law Force: F = ma = dp/dt Release: R = nb = dq/ds Torque: τ = Iα = s × F Strophence: σ = Jβ = t × R
Work | Repose Linear work: W = Fs Linear repose: Y = Rt Angular work: W = τθ Angular repose: Y = σφ
Power | Placidity Linear power: P = Fv Linear placidity: Z = Ru Angular power: P = τω Angular placidity: Z = σκ