# Euler Angles

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The Euler angles are a classical way to specify the orientation of an object in space with respect to a fixed set of coordinate axes. This Demonstration shows two of the several implementations of the Euler angles . The initial axes are indicated by the red, green, and blue arrows, while the final axes are indicated by the red, green, and blue spheres.

Contributed by: Frederick W. Strauch (August 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The Euler angles are used to define a sequence of three rotations , by the angles about the , , or , and axes, respectively. If the second rotation is about the axis, this is called the " convention". The net transformation is given by the matrix equation

.

This convention is used by Thornton and Marion [1] in Chapter 11.

If the second rotation is about the axis, this is called the " convention". The net transformation is given by the matrix equation

.

This convention is used by J. R. Taylor [2] in Chapter 10.

Both conventions are described by H. Goldstein [3] in Chapter 4.

See also Euler angles.

References

[1] S. T. Thornton and J. B. Marion, *Classical Dynamics of Particles and Systems*,* *Belmont, CA:* *Brooks/Cole, 2004.

[2] J. R. Taylor, *Classical Mechanics*, Mill Valley, CA: University Science Books, 2005.

[3] H. Goldstein, *Classical Mechanics,* Reading, MA: Addison-Wesley, 1980.

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