Dynamics and Stability – Exercises Module 4: Stability of Steady Motion

Course week(s) 4. Forces of Constraint and Stability of Steady Motion

Corresponding to each module, as described in the lectures section, the teachers handed out one or more sample problems. These are worked out examples that illustrate how to work with a certain method.

Next to the given sample problems, several recommended exercises are given. These exercises can be found in the textbook of this course (Analytical Mechanics, by Josef S. Tőrők). More on this textbook can be found in the readings section.

Sample problems:

Satellite in a four-dimensional universe In this sample problem, a satellite orbiting around a planet is analyzed. Now, the stability of the steady motion of the satellite is investigated using the energy approach of Lagrange. It is shown that there exists an ignorable coordinate, so that the Routhian function can be used.

Recommended exercises:

Solve the exercises in the provided order:

6.1
6.14 (make use of the answer to 2.60 if necessary and think twice before choosing a particular method of stability analysis)
6.31
6.43 (You can make use of the answer to 2.17 if you wish, but other methods could also be o.k.)
6.16 (take OA=AB=L and the angle between OA and OB as a generalised coordinate. Limit your study to the equilibrium point θ=0 and neglect gravity)
6.46 (Make use of the answer to 2.20 if you are unable to find a kinetic energy. This is an interesting problem, especially when it gets to the interpretation of the results!)
6.29 (Interesting and nice problem too!)

Answers exercises This file contains answers and hints corresponding to the following recommended exercises of this module: 6.1, 6.14, 6.16, 6.29, 6.31, 6.43, 6.46.

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