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• Euler_angles abstract "The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to represent the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or .Euler angles also represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate system. For instance, a first rotation about z by an angle α, a second rotation about x by an angle β, and a last rotation again about z, by an angle γ. These rotations start from a known standard orientation. In physics, this standard initial orientation is typically represented by a motionless (fixed, global, or world) coordinate system; in linear algebra, by a standard basis. Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system (extrinsic rotations) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation (intrinsic rotations). The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Without considering the possibility of using two different conventions for the definition of the rotation axes (intrinsic or extrinsic), there exist twelve possible sequences of rotation axes, divided in two groups: Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Tait–Bryan angles are also called Cardan angles, nautical angles, heading, elevation, and bank, or yaw, pitch, and roll. Sometimes, both kinds of sequences are called "Euler angles". In that case, the sequences of the first group are called proper or classic Euler angles.".
• Euler_angles thumbnail Eulerangles.svg?width=300.
• Euler_angles wikiPageExternalLink orilib.
• Euler_angles wikiPageExternalLink EulerAngles.html..
• Euler_angles wikiPageExternalLink eulermatrix.html.
• Euler_angles wikiPageExternalLink id584911325.
• Euler_angles wikiPageID "411492".
• Euler_angles wikiPageRevisionID "599701809".
• Euler_angles footer "Any target orientation can be reached, starting from a known reference orientation, using a specific sequence of intrinsic rotations, whose magnitudes are the Euler Angles of the target orientation. This example uses the z-x′-z″ sequence.".
• Euler_angles footer "Left: A three axes z-x-z gimbal where the external frame and external axis x are not shown and axes Y are perpendicular to each gimbal ring. Right: A simple diagram showing the Euler angles and where the axes Y of intermediate frames are located.".
• Euler_angles hasPhotoCollection Euler_angles.
• Euler_angles image "euler2a.gif".
• Euler_angles image "gimbaleuler.svg".
• Euler_angles image "gimbaleuler2.svg".
• Euler_angles image "intermediateframes.svg".
• Euler_angles title "Euler Angles".
• Euler_angles urlname "EulerAngles".
• Euler_angles width "150".
• Euler_angles width "160".
• Euler_angles width "170".
• Euler_angles width "180".
• Euler_angles subject Category:Analytic_geometry.
• Euler_angles subject Category:Angle.
• Euler_angles subject Category:Euclidean_symmetries.
• Euler_angles subject Category:Rotation_in_three_dimensions.
• Euler_angles type Abstraction100002137.
• Euler_angles type Attribute100024264.
• Euler_angles type EuclideanSymmetries.
• Euler_angles type Property104916342.
• Euler_angles type SpatialProperty105062748.
• Euler_angles type Symmetry105064827.
• Euler_angles comment "The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to represent the orientation of a frame of reference (typically, a coordinate system or basis) relative to another.".
• Euler_angles label "Angles d'Euler".
• Euler_angles label "Angoli di Eulero".
• Euler_angles label "Euler angles".
• Euler_angles label "Eulersche Winkel".
• Euler_angles label "Hoeken van Euler".
• Euler_angles label "Kąty Eulera".
• Euler_angles label "Ángulos de Euler".
• Euler_angles label "Ângulos de Euler".
• Euler_angles label "Углы Эйлера".
• Euler_angles label "زوايا أويلر".
• Euler_angles label "オイラー角".
• Euler_angles label "欧拉角".
• Euler_angles sameAs Eulersche_Winkel.
• Euler_angles sameAs Ángulos_de_Euler.
• Euler_angles sameAs Angles_d'Euler.
• Euler_angles sameAs Angoli_di_Eulero.
• Euler_angles sameAs オイラー角.
• Euler_angles sameAs 오일러_각.
• Euler_angles sameAs Hoeken_van_Euler.
• Euler_angles sameAs Kąty_Eulera.
• Euler_angles sameAs Ângulos_de_Euler.
• Euler_angles sameAs m.025495.
• Euler_angles sameAs Q751290.
• Euler_angles sameAs Q751290.
• Euler_angles sameAs Euler_angles.
• Euler_angles wasDerivedFrom Euler_angles?oldid=599701809.
• Euler_angles depiction Eulerangles.svg.
• Euler_angles isPrimaryTopicOf Euler_angles.