Euler's rotation theorem

English Etymology en Swiss mathematician Leonhard Euler 1707 1783 =, who proved the theorem in 1775. Proper noun en 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. en 2003 On the Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE, Proceedings https://books.google.com.au/books?id=afZQAAAAMAAJ&q=%22Euler%27s+rotation+theorem%22&dq=%22Euler%27s+rotation+theorem%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjGq6PVttbuAhVZb30KHZKQBAgQ6AEwFXoECEYQAg 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. en 2006 Patricia J. Lee Quantum Information Processing with Two Trapped Cadmium Ions https://books.google.com.au/books?id=Uw8eAQAAMAAJ&q=%22Euler%27s+rotation+theorem%22&dq=%22Euler%27s+rotation+theorem%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjGq6PVttbuAhVZb30KHZKQBAgQ6AEwEHoECD4QAg 40 University of Michigan 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: de Satz vom Fußball m Portuguese: pt Teorema de rotação de Euler m See also en Euler angle en Euler pole Further reading Euler angles Euler–Rodrigues formula Rotation around a fixed axis Rotation formalisms in three dimensions 3D rotation group