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Unformatted text preview: EEL 6935 Electronic Navigation Systems Homework Solution #3 Problem 1 Calculate the Schuler frequency for an inertial navigation system on Mars. See http://www.solarsystem.nasa.gov/ for information on Mars. Solution: On Mars, R = 3 , 397 , 000 m, and g = 3 . 693 m / sec 2 . s = r g R = s 3 . 693 m / sec 2 3 , 397 , 000 m = 1 . 04 10- 3 rad / sec T s = 2 rad s 1 min 60 sec = 100 . 4 min Problem 2 1. Show that the group refractive index, n g , can be written as n g = c dk d . (1) 2. Also show that the wave number, k , can be written as a function of the phase refractive index, n p : k = n p c (2) 3. Substitute (2) into (1), and show that n g = n p + dn p d . (3) Equation (3) is equivalent to equation (4.19) on page 137 of the text. Solution: Part 1: n g = c v g and v g = d dk implies n g = c dk d Part 2: n p = c v p and v p = k implies k = n p c 1 Part 3: Differentiate the result of part 2 with respect to : dk d = d d n n p c o = 1 c n p + dn...
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This note was uploaded on 01/15/2012 for the course EEL 6935 taught by Professor Staff during the Fall '08 term at University of Florida.
- Fall '08