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- Euler's_rotation_theorem abstract "In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a structure known as a rotation group.The theorem is named after Leonhard Euler, who proved it in 1775 by an elementary geometric argument. The axis of rotation is known as an Euler axis, typically represented by a unit vector . The extension of the theorem to kinematics yields the concept of instant axis of rotation.In linear algebra terms, the theorem states that, in 3D space, any two Cartesian coordinate systems with a common origin are related by a rotation about some fixed axis. This also means that the product of two rotation matrices is again a rotation matrix and that for a non-identity rotation matrix it must happen that: one of its eigenvalues is 1 and the other two are -1, or it has only one real eigenvalue which is equal to unity. The eigenvector corresponding to this eigenvalue is the axis of rotation connecting the two systems.".
- Euler's_rotation_theorem thumbnail Euler_AxisAngle.png?width=300.
- Euler's_rotation_theorem wikiPageExternalLink E478.pdf.
- Euler's_rotation_theorem wikiPageExternalLink E478.html.
- Euler's_rotation_theorem wikiPageExternalLink e478tr.pdf.
- Euler's_rotation_theorem wikiPageID "865138".
- Euler's_rotation_theorem wikiPageRevisionID "606715750".
- Euler's_rotation_theorem hasPhotoCollection Euler's_rotation_theorem.
- Euler's_rotation_theorem subject Category:Euclidean_symmetries.
- Euler's_rotation_theorem subject Category:Rotation_in_three_dimensions.
- Euler's_rotation_theorem subject Category:Theorems_in_geometry.
- Euler's_rotation_theorem type Abstraction100002137.
- Euler's_rotation_theorem type Attribute100024264.
- Euler's_rotation_theorem type Communication100033020.
- Euler's_rotation_theorem type EuclideanSymmetries.
- Euler's_rotation_theorem type Message106598915.
- Euler's_rotation_theorem type Property104916342.
- Euler's_rotation_theorem type Proposition106750804.
- Euler's_rotation_theorem type SpatialProperty105062748.
- Euler's_rotation_theorem type Statement106722453.
- Euler's_rotation_theorem type Symmetry105064827.
- Euler's_rotation_theorem type Theorem106752293.
- Euler's_rotation_theorem type TheoremsInGeometry.
- Euler's_rotation_theorem comment "In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a structure known as a rotation group.The theorem is named after Leonhard Euler, who proved it in 1775 by an elementary geometric argument.".
- Euler's_rotation_theorem label "Euler's rotation theorem".
- Euler's_rotation_theorem label "Pôle eulérien".
- Euler's_rotation_theorem label "Teorema de rotación de Euler".
- Euler's_rotation_theorem label "Теорема вращения Эйлера".
- Euler's_rotation_theorem label "مبرهنة الدوران لأويلر".
- Euler's_rotation_theorem label "歐拉旋轉定理".
- Euler's_rotation_theorem sameAs Teorema_de_rotación_de_Euler.
- Euler's_rotation_theorem sameAs Pôle_eulérien.
- Euler's_rotation_theorem sameAs m.03jpn0.
- Euler's_rotation_theorem sameAs Q681406.
- Euler's_rotation_theorem sameAs Q681406.
- Euler's_rotation_theorem sameAs Euler's_rotation_theorem.
- Euler's_rotation_theorem wasDerivedFrom Euler's_rotation_theorem?oldid=606715750.
- Euler's_rotation_theorem depiction Euler_AxisAngle.png.
- Euler's_rotation_theorem isPrimaryTopicOf Euler's_rotation_theorem.
