hw08 - AE 352: Aerospace Dynamics II, Fall 2008 Homework 8...

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AE 352: Aerospace Dynamics II, Fall 2008 Homework 8 Due Friday, October 31 Problem 1. Greenwood 6-26. Problem 2. Let the position of a mass m be specified by ( x,y,z ). The mass is in a potential field given by V = 1 2 k ( x 2 + y 2 + z 2 ) The mass is constrained according to 2 ˙ x + 3 ˙ y + 4 ˙ z + 5 = 0 a) Find the Lagrangian equations of motion in the form which includes constraint forces. b) Using the previous result, solve for the position of the mass as a function of time. Problem 3. Consider a satellite moving in a gravitational field with potential Φ. A pendulum of mass m and length l is attached to the satellite. Let the position and velocity of the satellite be known (given) functions of time. Let O xyz denote a coordinate frame attached to the satellite. a) Write an expression for the constraint on the mass. b) Is the system holonomic or non-holonomic? Is the constraint scleronomic or rheonomic? c) Denoting the
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hw08 - AE 352: Aerospace Dynamics II, Fall 2008 Homework 8...

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