# HW8 - = R sin ω.t 0(1 Express ω in terms of R and μ 2...

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MAE146: Astronautics – Homework Assigned: Wednesday, February 3 th , 2010 Due date: Friday , February 5 th , 2010, (at the beginning of the lecture) Please justify all of your answers. Write your answer cleanly with sentences and diagrams to explain. Don’t forget to write your name on your copy to receive credit. Problem 1 (10pts): Two-body problem with equal masses. Solve problem 2.1 in the textbook (current edition). The problem is about computing angular velocity in a 2-body problem. Relevant reading: chapter 2, sections 2.1-2.2 Problem 2 (20pts): On the center of mass and relative motion. 1. Let us consider the relative two-body problem: ¨ v r = - μ || v r || 3 v r . Show that the following motion (expressed in the coordinate system centered at the center of mass and inertially oriented) is a solution to the equations of motion when ω is chosen correctly. x ( t ) = R cos ω.t ; y ( t
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Unformatted text preview: ) = R sin ω.t ; 0 . (1) Express ω in terms of R and μ . 2. Using the previous solution, assume that the ±rst particle has mass ±ve times smaller than the second particle. Describe the motion of each particle relative to the center of mass inertial frame. Relevant reading: chapter 2, sections 2.1-2.2 Further problems (optional) Problem 2.2 about the three-body problem is quite interesting and would encourage you to think about it. In general the 3-body problem is non-integrable, that is there are no know general analytical solution. The described solution is one of the few analytic solutions available. Integrating the equations of motion, as indicated in in Problem 2.4 or 2.5 is also a good practive. Actually, you have the matlab code posted on the course website to easily solve these problems. 1...
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## This note was uploaded on 03/13/2010 for the course MAE 19100 taught by Professor Villac during the Winter '10 term at UC Irvine.

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