He ating Caus e s Po lar BEAR
to Lo s e S e ns e o f Dire c tio n
Polar Beacon Experiment and Auroral Research
Polar Beacon Experiment and Auroral Research
Gravity gradient stabilized with boom+tip ma
AOE 4140: Homework 6
1. (30) Consider the rigid body example did in class but
assume that the density is not constant and it varies in
space according to = r3 . Compute:
a) The mass of the rigid body
AOE 4140: Homework 4
1. (25) You are given the following matrix. Find the Euler axis (8) and angle of rotation (7).
Find the Euler parameters (quaternions) (10). You may use Matlab.
0.450484 0.780262
AOE 4140: Homework 2
Problem 1 (40). Consider the matrices:
1 2 3
1 1
1 1
=
A1 =
, A2 =
, A3 0 1 1
0 2
2 2
0 1 1
a) (10) Use Matlab to compute the eigenvalues and eigenvectors for all three matric
AOE 4140: Homework 8
1. (35) Consider the axisymmetric torque free rigid body example in the Lectures. Fill in the
gaps in the derivations as follows:
a) draw a figure showing the axisymmetric rigid b
AOE 4140: Homework 7 Solution Process
1. (60) Apply the PAT and Change of Basis theorem to the cylinder-panel
examined in class as follows.
a) Transfer the inertia matrix of the
cylinder to the mass c
AOE 4140: Homework 5
1. (40) A spacecraft has four attitude sensors, sensing four unit vectors, v k , k = 1, 2, 3,
4. We know that the first sensor (k = 1) is more accurate than the others, but we don
AOE 4140: Homework 4 Solution Process
1. (25) You are given the following matrix. Find the Euler axis of rotation (8) and the
corresponding angle of rotation (7). Find the Euler parameters (quaternion
AOE 4140: Homework 6 Solution Process
1. (30) Consider the rigid body example did in class but
assume that the density is not constant and it varies in
space according to = r3 . Compute:
a) The mass o
AOE 4140: Homework 8 Solution Process
1. (35) Consider the asymmetric torque free rigid body example worked in class. Fill in the
gaps in the derivations as follows:
a) draw a figure showing the axisy
AOE 4140: Homework 3
Problem 1 (25). An Earth-orbiting satellite is on an elliptical orbit with periapsis (point closest
to Earth label P) and apoapsis (point farthest away from Earth label A) altitud
AOE 4140: Homework 5
1. (40) A spacecraft has four attitude sensors, sensing four unit vectors, v k , k = 1, 2, 3,
4. We know that the first sensor (k = 1) is more accurate than the others, but we don
Chapter 1
Introduction
Spacecraft dynamics and control is a rich subject involving a variety of topics from
mechanics and control theory. In a rst course in dynamics, students learn that the
motion of
ICES at
Ice, Cloud and Land Elevation
Ice, Cloud and Land Elevation
satellite was launched 1/12/03
satellite was launched 1/12/03
into a 590 km sun-synch orbit
into a 590 km sun-synch orbit
Whats t
Co mpto n Gamma Ray Obs e rvato ry
Life time Re duc e d by ADCS Failure
At 35,000 lbs, CGRO was the largest LEO spacecraft
At 35,000 lbs, CGRO was the largest LEO spacecraft
ever launched on the Shu
P o we r Failure in ACS Affe c te d
S o lar Max Mis s io n (S MM)
Solar Max Mission was launched in
Solar Max Mission was launched in
early 1980 into a 574 km 28.5 orbit
early 1980 into a 574 km 28.
AOE 4140: Homework 7
1. (60) Apply the PAT and Change of Basis theorem to the cylinder-panel
examined in class as follows.
a) Transfer the inertia matrix of the
cylinder to the mass center of the pane