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hw03_solution

# hw03_solution - EEL 6935 Electronic Navigation Systems...

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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 . ω s = r g R = s 3 . 693 m / sec 2 3 , 397 , 000 m = 1 . 04 × 10- 3 rad / sec T s = 2 π rad ω 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 dω . (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 ω c (2) 3. Substitute (2) into (1), and show that n g = n p + ω dn p dω . (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 = dω dk implies n g = c dk dω Part 2: n p = c v p and v p = ω k implies k = n p ω c 1 Part 3: Differentiate the result of part 2 with respect to ω : dk dω = d dω n n p ω c o = 1 c n p + ω dn...
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hw03_solution - EEL 6935 Electronic Navigation Systems...

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