4431HW2for2017

4431HW2for2017 - Space Vehicle Dynamics Professor Richard...

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Space Vehicle Dynamics Professor Richard Longman Homework #2 Problem #1 A kg 3 10 rocket is to be launched vertically. Propellant is expelled at . sec / 2 kg Find the velocity needed e v so the rocked could just begin to rise. Problem #2 Find ) ( ) 0 ( t m m of a rocket such that the maximum burnout speed is two times the speed of the exhaust gas relative to the rocket. Problem #3 If each stage of a five-stage rocket has a 90 percent chance of firing properly, what is the probability that the payload will reach the desired height? Problem #4 3-1-3 Euler Angles means first rotate about the initial 3-axis, then rotate about the resulting 1-axis, and finally rotate about the resulting 3-axis, as shown in the figure. Compute 41 A , where [ ] [ ] ) 1 ( 41 ) 4 ( e A e = .

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Problem #5 Show by example that reversing the order of rotations produces a different resulting direction cosine matrix, so that the order of the rotations is important. Problem #6 Show that the determinant of a direction cosine matrix that relates a right handed coordinate system to another right handed coordinate system is equal to +1. And show
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