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, 2023-03-09 | Displacement + Time | Dischronment + Stance | Angle & Arc Length | Angle & Arc Duration | |
Stance / Distance Time / Distime | Displacement: s Time | distime: t | Dischronment: t Stance | distance: s | Angle length: θ = s/r Arc length: s | Angle duration: φ = t/q Arc duration: t | |
Radius | Period | Length radius r = S/(2π) = qv | Duration 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 | Wavenumber | Cross/Tangential velocity v⊥ = ds/dt = r×ω = r/q = S/T | Cross/Tangential lenticity w⊥ = dt/ds = q×κ = q/r = T/S | |||
Acceleration | Relentation | Radial acceleration a∥ = v2/r = rω2 = v/q = r/q² | Radial relentation b∥ = w2/q = qκ2 = w/r = q/r² | Angular acceleration α = dω/dt = aT/r | Angular relentation β = dκ/ds = bT/q | |
Tangential acceleration a⊥ = ω×v = Tdv/dt = rα | Tangential relentation b⊥ = Tdw/ds = qβ | ||||
Wavelength | Period | λ = S = 2πr = 2πvq | T = 2πq = 2πwr | λ = S = 2π/κ = 1/h | T = 2π/ω = 1/f | |
Revolutions | Repetitions Frequency | Circuncy | Revolutions N = θ/(2π) | Repetitions Z = φ/(2π) | Period frequency f = ω/(2π) = 1/T | Length frequency (circuncy) h = κ/(2π) = 1/λ | |
Displacement | Dischronment | s = s0 + vt | t = t0 + wx | θ = θ0 + ωt | φ = φ0 + κs | |
First Equation of Motion | v = v0 + at | w = w0 + bs | ω = ω0 + αt | κ = κ0 + βs | |
Second Equation of Motion | s = s0 + v0t + ½at² | t = t0 + w0s + ½bs² | θ = θ0 + ω0t + ½αt2 | φ = φ0 + κ0t + ½βs2 | |
Third Equation of Motion | v² = v0² + 2a∙(s – s0) | w² = w0² + 2b∙(t – t0) | ω² = ω0² + 2α∙(θ – θ0) | κ² = κ0² + 2β∙(φ – φ0) | |
Inertia | Facilia | Mass – linear inertia: m = 1/n | Vass-linear facilia: n = 1/m | Angular inertia: I = mr2 | Angular facilia: J = nq2 | |
Momentum | Levamentum | Momentum: p = mv | Levamentum: q = nw | Angular momentum: L = Iω | Angular Levamentum: Γ = Jκ | |
Kinetic Energy and Lethargy | Kinetic energy: EK = ½mv2 | Kinetic lethargy: LK = ½nw2 | 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 = F ∙ s | Linear repose: Y = R ∙ t | Angular work: W = τ ∙ θ | Angular repose: Y = σ ∙ φ | |
Power | Placidity | Linear power: P = F ∙ v | Linear placidity: Z = R ∙ w | Angular power: P = τ ∙ ω | Angular placidity: Z = σ ∙ κ |