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Unformatted text preview: AE 352: Aerospace Dynamics II, Fall 2008 Midterm Exam 1 Friday, October 3 11:00  11:50 am Closed book examination – no notes, calculators. Problem 1. In this problem, you will complete multiple steps to find the equations of motion for a spherical pendulum of mass m and length l . Figure 1: Spherical pendulum. (a) Find the angular velocity ω of the pendulum [20 pts]. Solution. ω = ˙ φ k ˙ θ e φ where k = cos θ e r + sin θ e θ . Thus ω = ˙ φ cos θ e r + ˙ φ sin θ e θ ˙ θ e φ (b) Find the velocity v of the mass [15 pts]. Solution. v = v rel + ω × r = 0 + ( ˙ φ cos θ e r + ˙ φ sin θ e θ ˙ θ e φ ) × l e r = ˙ θl e θ + ˙ φl sin θ e φ Page 1 of 3 AE 352: Aerospace Dynamics II, Fall 2008 (c) Find the acceleration a of the mass [25 pts]. Solution. a = a rel + ω × ω × r + ˙ ω × r + 2 ω × v rel where a rel = 0 and v rel = 0 After performing the big cross product for ω × ω × r , we get: ω × ω × r = l ( ˙ θ 2 ˙ φ 2 sin 2 θ )...
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This note was uploaded on 09/16/2009 for the course AE ae352 taught by Professor Sri during the Spring '09 term at University of Illinois at Urbana–Champaign.
 Spring '09
 SRI

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