Motion Equations

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

Parallel Equations of Motion

RA Gillmann, 2020-06-19Displacement + TimeDischronment + StanceSpatial Angles + TimeTemporal Angles + Stance
Stance / Distance |

Time / Distime

Displacement: s

Time | distime: t

Dischronment: t

Stance | distance: s

Spatial angle: θ = s/r

Temporal arc: t

Temporal angle: φ = t/q

Spatial arc: s

Radius | PeriodSpatial radius

r = S/(2π) = qv

Temporal radius

q = T/(2π) = rw

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 = w/q = 1/r

Velocity | Lenticity | WavenumberCross/Tangential velocity

v = ds/dt = r×ω = r/q = S/T

Cross/Tangential lenticity

w = dt/ds = q×κ = q/r = T/S

Acceleration | RelentmentRadial acceleration

a = v2/r =2 = v/q = r/q²

Radial relentment

b = w2/q =2 = w/r = q/r²

Angular acceleration

α = dω/dt = aT/r

Angular relentment

β = dκ/ds = bT/q

Tangential acceleration

a = ω×v = Tdv/dt = rα

Tangential relentment

b = Tdw/ds = qβ

 
Wavelength | Periodλ = S = 2πr = 2πvqT = 2πq = 2πwrλ = S = 2π/κ = 1/hT = 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 | Dischronments = s0 + vtt = t0 + wxθ = θ0 + ωtφ = φ0 + κs
First Equation of Motionv = v0 + atw = w0 + bsω = ω0 + αtκ = κ0 + βs
Second Equation of Motions = s0 + v0t + ½at²t = t0 + w0s + ½bs²θ = θ0 + ω0t + ½αt2φ = φ0 + κ0t + ½βs2
Third Equation of Motionv² = v0² + 2a∙(s s0)w² = w0² + 2b∙(t t0)ω² = ω0² + 2α∙(θ θ0)κ² = κ0² + 2β∙(φ φ0)
Inertia | FaciliaMass – linear inertia: m = 1/nVass-linear facilia: n = 1/mAngular inertia: I = mr2Angular facilia: J = nq2
Momentum | LevamentumMomentum: p = mvLevamentum: q = nwAngular momentum: L = IωAngular Levamentum: Γ = Jκ
Kinetic Energy and LethargyKinetic energy: EK = ½mv2Kinetic lethargy: LK = ½nw2Angular energy EA = ½Iω2Angular lethargy LA = ½Jκ2
Newton’s Second LawForce: F = ma = dp/dtRelease: R = nb = dq/dsTorque: τ = Iα = s × FStrophence: σ = Jβ = t × R
Work | ReposeLinear work: W = FsLinear repose: Y = RtAngular work: W = τθAngular repose: Y = σφ
Power | PlacidityLinear power: P = FvLinear placidity: Z = RwAngular power: P = τωAngular placidity: Z = σκ