Rigid Body Nutation. Euler’s equations describe the motion of the principal-axis components of the angular velocity of a freely rotating rigid body (such as a space station), as seen by an observer rotating with the body (the astronauts, for example). This motion is called nutation. If the angular velocity components are denoted by
The trajectory of a solution
a. Show that each trajectory of this system lies on the surface of a (possibly degenerate) sphere centered at the origin
b. Find all the critical points of the system, i.e. all points
c. Show that the trajectories of the system lie along the intersection of a sphere and an elliptic cylinder of the form
d. Using the results of parts (b) and (c), argue that the trajectories of this system are closed curves. What does this say about the corresponding solutions?
e. Figure
Figure
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Fundamentals of Differential Equations and Boundary Value Problems
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage