Constant velocity motion

A function model:  p(t) = V*t + P0

 A 1st order differential equation model: p(t) = V

 A 2nd order differential equation model: p’’(t) = 0


A falling object

Newton’s model: r’’(t) = -G*M*MEarth/r(t)2

A simplified model: r’’(t) = -10


Motion of a rigid object




Atmospheric drag for an object

Air density:  D = 1.4*(1 – altitude/30,000) for altitude < 30,000

Force of atmospheric drag:  Fdrag = Cdrag * D * v2 * cs / 2


Airplane lift and drag

CL = 0.5 + 0.1*AoA

Flift = CL*D** v2 * s

CD = (5 - AoA )*1 + 0.7 for AoA <= 5

CD = (AoA - 5 )*1 + 0.7 for AoA > 5

Fdrag = CD*D** v2 * s


Electrical components

A resistor: vR(t) = i(t)R

A capacitor: vC’(t) = i(t)/C

An inductor vI(t) = i’(t)L


Mechanical components

A spring:  Fs(t) = -K * p(t)

A hydraulic damper:  Fd(t) = -cp’(t)






Sliding friction

Coulomb or sliding friction:  FC(t) = -mNsign(p’(t))


Programmed models

We have programmed models for rocket thrusters, airplane thrust, aircraft elevator torque, electrical impulses, and rocky roads, by directly specifying their values at each subinterval in the computation.





Laws of physics

The law of gravity: F = GM1M2/R2

The 2nd law of motion:  F=MA

The 2nd law of rotation:  T=a’’/I


Kirchoff’s Electrical Circuit Laws

Kirchoff’s voltage law:  The sum of the voltages around a loop in a circuit is zero.

Kirchoff’s current law: The sum of currents entering a node in a circuit is zero.