Home Courses Dynamics and Stability Course materials Lectures 4. Forces of Constraint and Stability of Steady Motion

4. Forces of Constraint and Stability of Steady Motion

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

This module expands the Lagrange approach to find the equations of motion of rigid bodies by introducing ignorable coordinates. Furthermore, the Routhian function is given. This function is equivalent to the Lagrangian, without the ignorable coordinates. Steady motion for non-ignorable coordinates is explained and by defining dissipative forces, the Rayleigh dissipation function is derived.

Lagrange multipliers are explained. These can be used to investigate the reaction forces in a system or to analyze systems where it’s difficult to identify the degrees of freedom.
Next, the stability of systems is elaborated. The conditions that have to be met for a system to be stable are given and it is shown how to analyze stability by using a linearization of the system.

One sample problem is given in the module and can be found in the exercises of this module.

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Slides: Module 4 lecture 1
Slides: Module 4 lecture 2
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