1. 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

2. 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 0 2 + 2 a (d – d 0 ) final velocity with constant acc tan = opp /adj direction of travel

3. 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 = 0. 2. F = ma 3. F a on b = -F b on a (for every action there is an = and opposite reaction)

4. A Ball in the Trunk

5. Dead Reckoning Direction Distance

6. Roll, Pitch, and Yaw

7. X, Y, Z Roll, Pitch, Yaw

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

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

10. An “Artificial Horizon” is a Mechanical Gyroscope

11. Optical gyroscopes Ring Laser gyroscope Fiber Optic Loop gyroscope

12. 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

13. Circuits can Differentiate and Integrate

14. Differentiating Circuit

15. Integrating Circuit

16. Inertial Navigation System

17. Accelerometer on a microchip

18. The engineering term is “catastrophic failure”

19. Credits INS http://www.fauskes.net/media/pgftikzexam ples/PNG/inertial-navigation-system.png Differenitating and Integrating Circuits http://www.physics.ucla.edu/demoweb/de momanual/electricity_and_magnetism/ac_c ircuits/rc_integration_and_differentiation.ht ml

20. Credits II Gyroscope diagram http://innergyro.com/images/800px- 3D_Gyroscope%5B1%5D.png X, Y, Z and Roll, Pitch, Yaw diagram http://developer.valvesoftware.com/w/ima ges/7/7e/Roll_pitch_yaw.gif

21. Credits III Artificial Horizon http://www.computermuseum.li/Testpage/Sperry HorizonIndicatorGyroscope.jpg Accelerometer on a microchip http://clifton.mech.northwestern.edu/~me381/Gyr oscope.gif Ring Laser gyroscope http://media-2.web.britannica.com/eb- media/16/78616-004-BDBE9561.jpg