Euler's rotation theorem

English

Etymology

Named after Swiss mathematician Leonhard Euler (1707–1783), who proved the theorem in 1775.

Proper noun

Euler's rotation theorem

1. (geometry) A theorem which states that, in 3-dimensional space, any displacement of a rigid body such that some point on it remains fixed is equivalent to a single rotation about some axis that runs through said point.
   • 2003, On the Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE, Proceedings, page 136:

     Otherwise, this approach will be valid subject to the previous rotation of the axes according to Euler's Rotation Theorem.

   • 2005, JSME International Journal: Mechanical systems, machine elements and manufacturing, Volume 48, Issue 4, Japan Society of Mechanical Engineers, page 501,

     According to Euler's rotation theorem, any finite rotation transformations may be described using only three angles defined as Euler angles.

   • 2006, Patricia J. Lee, Quantum Information Processing with Two Trapped Cadmium Ions, University of Michigan, page 40:

     From Euler's rotation theorem we know that an arbitrary rotation in three dimensions can be parameterized by three independent variables called the Euler angles, each rotating around an orthogonal axis.

Translations

mathematical theorem

• German: Satz vom Fußball m
• Portuguese: Teorema de rotação de Euler m

See also

• Euler angle
• Euler pole

Further reading

• Euler angles on Wikipedia.Wikipedia
• Euler–Rodrigues formula on Wikipedia.Wikipedia
• Rotation around a fixed axis on Wikipedia.Wikipedia
• Rotation formalisms in three dimensions on Wikipedia.Wikipedia
• 3D rotation group on Wikipedia.Wikipedia