AE 352: Aerospace Dynamics II, Fall 2008
Homework 1
Due Friday, September 5
Problem 1. Show that ki j kpq = ip jq - iq jp through the following steps: a) Using the facts below, show that [im jn (em en )] [pr qs (er es )] = ki j kpq Facts: i. ei e j = ki j

AE 352: Aerospace Dynamics II, Fall 2008
Midterm Exam 2
Friday, November 7 11:00 - 11:50 am Closed book examination no notes, calculators.
Problem 1. A particle of mass m in a uniform gravitational field is constrained to lie on a parabolic surface given

AE 352: Aerospace Dynamics II, Fall 2008
Midterm Exam 2
Friday, November 7 11:00 - 11:50 am Closed book examination no notes, calculators.
Problem 1. A particle of mass m in a uniform gravitational field is constrained to lie on a parabolic surface given

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

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

AE 352: Aerospace Dynamics II, Fall 2008
Homework 10
Due Wednesday, 12/10/2008
Problem 1. Greenwood 9.3 Problem 2. (a) Determine a 321 (i.e. or ZYX) rotation matrix R representing the rotation of a body relative to an inertial frame with the given Euler a

AE 352: Aerospace Dynamics II, Fall 2008
Homework 9
Due Wednesday, November 19
Problem 1. For the matrix K, and the vector q 3 1 0 1 K = 1 3 1 q = -2 0 1 2 1 (a) Evaluate Kq, q T K, q T K T , and 1 q T Kq. 2 (b) Determine whether the matrix K is positive

AAE 250
Homework 8 Solutions http:/nsgsun.aae.uiuc.edu/AAE250 1. Solution (a) The constraint equation is simply
x 2 + y 2 + z 2 = b2
This constraint expresses the fact that the mass is located at a distance the main satellite. (b) The constraint is holono

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 1 V = k(x2 + y 2 + z 2 ) 2 The mass is const

AE 352: Aerospace Dynamics II, Fall 2008
Homework 7
Due Friday, October 24
Problem 1. Write down the constraint equations for each of the following descriptions. Note that you must first identify the generalized coordinates. In your answer, also specify t

AE 352: Aerospace Dynamics II, Fall 2008
Homework 6
Due Friday, October 17
Problem 1. Derive equation 6-88 in Greenwood, and describe each term. In other words, say as much as you can about the qualitative meaning of each term in the general equations of

AE 352: Aerospace Dynamics II, Fall 2008
Homework 6
Due Friday, October 17
Problem 1. Derive equation 6-88 in Greenwood, and describe each term. In other words, say as much as you can about the qualitative meaning of each term in the general equations of

AE 352: Aerospace Dynamics II, Fall 2008
Homework 5
Due Friday, October 10
Problem 1. Using x1 and x2 as coordinates, obtain the kinetic and potential energy of the system of sliding blocks shown in Figure 1 (assume no friction).
Figure 1: A system of sli

AE 352: Aerospace Dynamics II, Fall 2008
Homework 5
Due Friday, October 10
Problem 1. Using x1 and x2 as coordinates, obtain the kinetic and potential energy of the system of sliding blocks shown in Figure 1 (assume no friction). Problem 2. Find the diffe

AE 352: Aerospace Dynamics II, Fall 2008
Homework 4
Due Friday, September 26
Problem 1. Consider a mass resting on the floor, and attached to a wall with a spring and damper. Let m = 4, k = 4, c = 1. A force F acts on the particle. (Note this is a 1D prob

AE 352: Aerospace Dynamics II, Fall 2008
Homework 4
Due Friday, September 26
Problem 1. Consider a mass resting on the floor, and attached to a wall with a spring and damper. Let m = 4, k = 4, c = 1. A force F acts on the particle. (Note this is a 1D prob

AE 352: Aerospace Dynamics II, Fall 2008
Homework 3
Due Friday, September 19
Problem 1. Find the free and forced responses of the following system: d2 y dy du + 4 + 4y = 3 + 2u 2 dt dt dt where u(t) = 0 for t < 0 and u(t) = e-3t for t 0. Solution. There a

AE 352: Aerospace Dynamics II, Fall 2008
Homework 3
Due Friday, September 19
Problem 1. Find the free and forced responses of the following system: d2 y dy du + 4 + 4y = 3 + 2u 2 dt dt dt where u(t) = 0 for t < 0 and u(t) = e-3t for t 0. Problem 2. Proble

AE 352: Aerospace Dynamics II, Fall 2008
Homework 2
Due Friday, September 12
Problem 1. Problem 2.6 in Greenwood. Problem 2. Problem 2.8 in Greenwood. Solution. We use Eqn. 2-106 in Greenwood to find the absolute acceleration of point P, which is in motio

AE 352: Aerospace Dynamics II, Fall 2008
Homework 2
Due Friday, September 12
Problem 1. Problem 2. Problem 3. Problem 4.
Problem 2.6 in Greenwood. Problem 2.8 in Greenwood. Problem 2.11 in Greenwood. Problem 2.19 in Greenwood.
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AE 352: Aerospace Dynamics II, Fall 2008
Homework 1
Due Friday, September 5
Problem 1. Show that ki j kpq = ip jq - iq jp through the following steps: a) Using the facts below, show that [im jn (em en )] [pr qs (er es )] = ki j kpq Facts: i. ei e j = ki j