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28: Euler’s Equations

Last updated

May 11, 2024
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- 27.6: Stability of Top Spinning about Vertical Axis
- 28.1: Introduction to Euler’s Equations

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28.1: Introduction to Euler’s Equations
We’ve just seen that by specifying the rotational direction and the angular phase of a rotating body using Euler’s angles, we can write the Lagrangian in terms of those angles and their derivatives, and then derive equations of motion. These can be solved to describe precession, nutation, etc.
28.2: Free Rotation of a Symmetric Top Using Euler’s Equations
This is a problem we’ve already solved, using Lagrangian methods and Euler angles, but it’s worth seeing just how easy it is using Euler’s equations.
28.3: Using Energy and Angular Momentum Conservation
We can also gain some insight into the motion of the free spinning top just from conservation of energy and angular momentum.
28.4: The Asymmetrical Top

Thumbnail: Classic Euler angles geometrical definition. The xyz (fixed) system is shown in blue, the XYZ (rotated) system is shown in red. The line of nodes (N) is shown in green (CC BY-SA 3.0; Lionel Brits via Wikipedia)

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