AE403 Homework #2:
Alternative Representations of Rotation
Koki Ho
(due at the beginning of class on Tuesday, February 21)
1. (12 points) Be able to construct a rotation matrix from Euler Angles. Consider the XYZ
body-axis Euler Angle sequence: frame 1 is
AE403 Homework #3:
Dynamics, Part 1
Koki Ho
(due at the beginning of class on Tuesday, March 14)
1. (20 points) Be able to derive Eulers equation. This proof is the most difficult one that I will
ask you to attempt all semester. It is a beautiful way of b
AE403 Homework #4:
Dynamics, Part 2
Koki Ho
(due at the beginning of class on Tuesday, April 18)
1. (15 points) Be able to derive criteria that guarantee passive spin stabilization under energy
dissipation. Consider a torque-free axisymmetric spacecraft.
AE403 Homework #1:
Rotation Matrices
Koki Ho
(due at the beginning of class on Tuesday, Jan 31)
1. (15 points)Be able to write a rotation matrix by inspection. The orientation of frame k written
in the coordinates of frame j is the rotation matrix
i
h
Rkj
AE323 Homework assignment #5 Due on Friday March 4 at class time
Topic: Beam torsion
Reminder: Dont forget to include your name in every Matlab .m file and in the title of every plot you
create (using the command title)
Problem 1. Solve problem 12.8 in th
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 #3 Due on Friday February 19 at class time
Topic: Bending and extension of beams
Recall: the textbook can be found at the following link
http:/proquest.safaribooksonline.com.proxy2.library.
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
HWK 10 Solution
Problem 1
(a) The BVP for this problem is
GDE:
BCs:
EIw Pw 0
w0 w0 w L w L 0
The general solution to this equation is:
w x A sin x B cos x Cx D, =
P
EI
Substituting the BCs:
w0 0 B D 0
w0 0 A C 0
wL 0 A sin L B cos L CL D 0
w L 0 A2 sin L
AE 323 - Homework assignment #2
Friday February 5th, 2016
Due on Friday, February 12th, 2016 in class
Topic: Computer-based symbolic math and plotting, and calculation of area properties
Using the symbolic math software of your choice (Mathematica or Matl
AE323 Homework #6 Due on Friday March 11 (by 10am)
Topic: Approximate solutions of thin-walled beam torsion
Problem 1. Solve problem 13.2. Provide details on your derivations.
Problem 2. Solve problem 13.3 a
AE323 Homework #10 Friday, April 29, 2016
Due by 5pm on Monday, May 9, 2016
Topic: Beam buckling
Problem 1. Consider the buckling problem shown in the figure below. The beam is of length L,
stiffness
E a
AE 312
Assignment 1
J. C. Dutton
1. Water ( = 998 kg/m3) flows steadily and at low speed through a circular tube with inside diameter of
50 mm, as shown below. A smoothly contoured plug of 40 mm diameter is held in place at the end of
the tube by force F,
AE 312
Assignment 4
J. C. Dutton
For this assignment assume that the flow is everywhere isentropic except across any normal shock waves
that may occur.
1. Air is flowing at a Mach number of 0.5 in a two-dimensional channel at a location where the area is
AE 312
Assignment 5
J. C. Dutton
1. Due to a mis-communication, a machinist fabricates a diverging-converging (instead of c-d) nozzle
with diameter dimensions shown below. At a particular operating condition, the pressure and
temperature in the large air
AE 312
Assignment 3
J. C. Dutton
1. A bullet travels down a gun barrel that is open to stationary air at P = 100 kPa, T = 300 K, as shown.
But because of a mis-fire, the bullet velocity is only 100 m/s (instead of the usual 1100 m/s).
(a) Does a normal sh
AE 312
Assignment 2
J. C. Dutton
1. Find expressions (as functions of ) or constant values for the normal shock functions D/U =
VRU/VRD, PD/PU, TD/TU, MRD, and PORD/PORU in the asymptotic high-Mach number limit as
. Evaluate these limits for = 1.4 and co
1
AE 321
Homework 7
Due in class on October 21, 2016
Problem 1.
Consider a rectangular plate of length, l, height, h, and width, t. The plate is composed of a
linearly elastic, isotropic, homogeneous material.
(A)
The body is subjected to a uniform pressu
Topic 2: Finite element formulation and analysis for 1-D Poisson problems
Problem 2.1: FEA of a bi-material axially loaded bar
Consider the bi-material axially loaded bar structure of length 2L described in Figure 2.1.
It is discretized with 5 nodes and 4
Problem 1.3
a) Find the exact solution for the beam torsion problem shown above. The loading consists of a
uniformly distributed torque mo and a point torque M applied at the end (x=L). The beam is
fixed at x=0.
b) Two of the following four basis
m0 (Nm/m