Physics Models Results

Orbits, Satellites, Rockets F = m ∙ p’’ Fg = G ∙ m1 ∙ m2 / r^2	bodies in freefall p’’ = G ∙ m2 / r^2 satellites Apollo trajectory Juno trajectory
Electrical Circuits vR = i ∙ R vC’ = i / C iL’ = V / L	low-pass filter iL’ = (vS – vC)/L vC’ = ( iL + (vS - vC/R))/C
Rigid Body Dynamics F = m ∙ p’’ Г = I ∙ a’’ Fs = - k ∙ p Fd = - m ∙ v Fl = 0.5 ∙ d ∙ v^2 ∙ s ∙ CL	auto suspension VEX robot ia’=(va - R×ia - Kb× w)/L q’=w w’ = ( Km× ia - B× w )/ J airplane simulator

Heat Transfer q = - k ∙ (∂T / ∂x, ∂T / ∂y) T = (1/c) ∙ heat energy / vol.	time-dependent heat transfer ∂T/ ∂t = C∙(∂^2T/ ∂x^2, ∂^2T/ ∂y^2)
The Wave Equation F = m ∙ p’’	vibrating string ∂^2u / ∂^2t = C∙∂^2u/∂x vibrating surface ∂^2u / ∂^2t = C∙(∂^2u/∂x, ∂^2u/∂y)
Stress and Strain

Fluid Dynamics F = m ∙ p’’ Г = I ∙ a’’ Reynold’s Transport Thrm t = F / A = m (v/L)	Navier-Stokes Equations	. .
Maxwell’s Equations	electromagnetic radiation model = Maxwell’s equations