Day 48, Tuesday, 3 November, 2015 Inertial Navigation Systems The magical, mysterious, always everywhere box The ball in the trunk Dead Reckoning: Direction and Distance Roll, Pitch, Yaw and X, Y, Z Gyroscopes Mechanical Optical Accelerometers iPhone Inertial Navigation Units

Important motion equations avg v = ∆d/∆t = d f – d i / t f - t i avg a = ∆v/∆t = v f – v i / t f – t i d = d 0 + v t position with constant velocity d = d 0 + v 0 t + ½ a t 2 position with constant acceleration v = v 0 + a t velocity with constant acceleration d = d 0 + ½ (v + v 0 )t final position with constant velocity v 2 = v a (d – d 0 ) final velocity with constant acc tan = opp /adj direction of travel

Newton’s 3 Laws of Motion 1. Inertia: An object at rest will remain at rest. An object moving will move in a straight line with constant speed, if and only if the net force acting on it = F = ma 3. F a on b = -F b on a (for every action there is an = and opposite reaction)

A Ball in the Trunk

Dead Reckoning Direction Distance

Roll, Pitch, and Yaw

X, Y, Z Roll, Pitch, Yaw

Gyroscope Inertia keeps the spinning mass from moving out of the plane of rotation

Gyroscopic Stabilization Gyroscopic Stabilization is how bicycles stay up Old navy trick

An “Artificial Horizon” is a Mechanical Gyroscope

Optical gyroscopes Ring Laser gyroscope Fiber Optic Loop gyroscope

Inertial Navigation Unit using Gyroscopes and accelerometers Gyroscope (roll)  differentiating circuit Gyroscope (pitch)  differentiating circuit Gyroscope (yaw)  differentiating circuit Accelerometer (X)  integrating circuit Accelerometer (Y)  integrating circuit Accelerometer (Z)  integrating circuit

Circuits can Differentiate and Integrate

Differentiating Circuit

Integrating Circuit

Inertial Navigation System

Accelerometer on a microchip

The engineering term is “catastrophic failure”

Credits INS ples/PNG/inertial-navigation-system.png Differenitating and Integrating Circuits momanual/electricity_and_magnetism/ac_c ircuits/rc_integration_and_differentiation.ht ml

Credits II Gyroscope diagram 3D_Gyroscope%5B1%5D.png X, Y, Z and Roll, Pitch, Yaw diagram ges/7/7e/Roll_pitch_yaw.gif

Credits III Artificial Horizon HorizonIndicatorGyroscope.jpg Accelerometer on a microchip oscope.gif Ring Laser gyroscope media/16/ BDBE9561.jpg