## 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

F=MA

T=a’’/I

#### 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.