AAE 270, FINAL
December 2002
No calculators, Show all steps
Problem 1 (15 points)
Consider the following PDE where F and G are positive constants
2 w/r2 + F 2 w/c2 = G w2
a) Identify the rank of the PDE, and whether it is coupled, and whether it is linear
AAE 270 Computational Methods in Aerospace Engineering
Fall 2000 Final Exam Duration: 3 hours
Closed Notes Closed Books No Calculator
Chapter 4 questions (50 points)
Problem 1) (15 points)
Using the Taylor series expansion for a function
f(x+ x) = f(x) +
AE 352: Aerospace Dynamics II, Fall 2011
Homework 4
Due 5.00 pm, Friday, September 23th
Problem 1. For the setup shown and generic spring stiffness constant k, damping
coefficient c, mass M, constant forcing g, constant angle , and general initial
positio
AE 352: Aerospace Dynamics II, Fall 2011
Homework # 1 Solution
Due 5.00 pm, Friday, September 2nd
Problem 1. Show that ki j kpq = ip jq iq jp through the following steps:
1. Show
[im jn (em en )] [pr qs (er es )] = ki j kpq
(1)
using the following facts:
AE 352: Aerospace Dynamics II, Fall 2011
Homework 2
Due 5.00 pm, Friday, September 9
Problem 1. A particle, denoted by P, slides on a circular table as shown in Fig. 1.
The position of the particle is known in terms of the radius r and the angle , where
r
AE 352: Aerospace Dynamics II, Fall 2011
Homework 3
Due 5.00 pm, Friday, September 16
Problem 1.
Consider a satellite that is orbiting the Earth in a circular orbit of radius R from the
center of the Earth. The satellite can be modeled as a point at O0 th
1
AE 403: Spacecraft Attitude Control
Homework #1: Attitude Representations
Due: Beginning of class on Friday, February 8th
1. 2-Dimensional Frame Rotations. Recall from lecture that the orientation of frame k in the
coordinates of frame j can be expresse
1
AE 403: Spacecraft Attitude Control
Homework #2: Quaternion Representations
Due: 5pm on Friday, March 8th
1. Rotation Matrix from Exponential Coordinates. Recall from lecture that any rotation matrix can
be generated by a single rotation of some angle a
1
AE 403: Spacecraft Attitude Control
Homework #3: Dynamics
Due: 5pm on Friday, April 19th
( )
1. Kinematic differential equations of Euler Angles. For the sequence of ( )
( ) to frame B from frame A, derive the following kinematic differential equation:
1
AE 403: Spacecraft Attitude Control
Homework #4: Controls
Due: 5pm on Thursday, May 2nd
1. Passive Stabilization with Energy Dissipation. In class, we derived the system equations of
motion for an axisymmetric spinning satellite. When considering energy
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AE323 Applied Aerospace Structures Fall 2016
Homework 3 Chapter 2.1 Moments of area, Axial force, Bending
SOLUTIONS
1. (a) The Youngs modulus of the three sections are
First, the Youngs modulus of aluminum is chosen to be the reference modulus.
The areas
AE323 Applied Aerospace Structures Spring 2016
Homework 1 Chapter 1 Stresses and Strains
SOLUTIONS
1.
2.
3.
4.
*Students may solve using any of the three methods for part a
4a) Using the principal value (eigenvalue) theory:
det = 0
1 2 0
= 2 4 0
0 0 0
1
AE323 Homework assignment #8
Due on Friday April 15, 2016, at class time
Topic: Castiglianos method
Note: As always, provide a printout of any symbolic math worksheet you might use, and include your
name in t
AE323 Homework assignment #9 Friday April 15, 2016
Due in class on Friday April 22, 2016
Topic: Castigliano method for statically indeterminate problems
Problem 1
Consider a beam of length L, stiffness E, den
AE323 Homework Assignment #1 Friday January 29, 2016
Due on Friday, February 5, 2016 in class
Topics: Stresses and Cauchy relations
Problem 1.
Consider the 2D problem of a rectangular linearly elastic solid (
AE 323 Homework Assignment #2
Matlab Solutions
% Problem 1
x=linspace(0,1,800); %array containing 100 equally spaced values of x
a=0; % set a to 0
f_a0=(2*x.^3).*sin(x)+a.*x.^2.*heaviside(x-2/3)+5*a*x-1; % compute f(a=0) for
each value of x
a=2; % set a t
AE323 Homework assignment #4 Due on Friday, February 26 at class time
Topic: Beam bending and extension
Problem 1
Consider the following cantilever beam bending problem. The beam is symmetric, homogeneous,
linearl
AE323 Homework Assignment #7
Due at class time on Friday, April 8, 2016
Topic: Principle of virtual work
Note: For some of the symbolic math manipulations, feel free to use mupad available from
Matlab (just e
AAE 221 Aerospace Structures II Spring 2004 Chapter 4 Introduction to Buckling Solution 1. We can neglect y effects and assume s y = 0 .
From the beam equation, w' '+
4p 2 EI P w = 0 , we get Pcr = . EI S2
In addition, s x = s y = 0 (plane stress in x-y p
AAE 221 Aerospace Structures II Spring 2004 Chapter 3.1 Work and Potential Energy Principles Solution 1. Consider the free body diagrams below. The circular object on the left represents the upper mass while the circular object on the right represents the
AAE 221 Structures II Spring 2004 Chapter 2.3 Beam shearing 1. First the location of the centroid and the moments of inertia must be found
1 1 z i Ai = 98t 2 A The moments of inertia are y cm =
2 i
2 2 t 1 2 25t ( 2.5t ) + 48t 2 = 6.62t
(
)
(
)
25t t 3