| http://dbpedia.org/ontology/abstract
|
In geometry, various formalisms exist to e … In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space. According to Euler's rotation theorem the rotation of a rigid body (or three-dimensional coordinate system with the fixed origin) is described by a single rotation about some axis. Such a rotation may be uniquely described by a minimum of three real parameters. However, for various reasons, there are several ways to represent it. Many of these representations use more than the necessary minimum of three parameters, although each of them still has only three degrees of freedom. An example where rotation representation is used is in computer vision, where an automated observer needs to track a target. Consider a rigid body, with three orthogonal unit vectors fixed to its body (representing the three axes of the object's local coordinate system). The basic problem is to specify the orientation of these three unit vectors, and hence the rigid body, with respect to the observer's coordinate system, regarded as a reference placement in space.egarded as a reference placement in space.
, En geometría, existen varias formalizacion … En geometría, existen varias formalizaciones para expresar una rotación en tres dimensiones como una matemática. En física, este concepto se aplica a la mecánica clásica, donde la cinemática rotacional (o angular) es la ciencia que describe cuantitativamente un movimiento puramente rotativo. La orientación de un objeto en un instante dado se describe con las mismas herramientas, ya que se define como una rotación imaginaria a partir de una ubicación de referencia en el espacio, en lugar de una rotación realmente observada de una ubicación anterior en el espacio. De acuerdo con el teorema de rotación de Euler, la rotación de un cuerpo rígido (o sistema de coordenadas tridimensional con el origen fijo) se describe mediante una única rotación respecto a un determinado eje. Dicha rotación se puede describir de forma única mediante un mínimo de tres parámetros reales. Sin embargo, por varias razones, hay varias formas de representarlo. Muchas de estas notaciones utilizan más del mínimo necesario de tres parámetros, aunque cada una de ellas tiene solo tres grados de libertad. Un ejemplo donde se usa la representación de las rotaciones es en la visión artificial, donde un observador automático necesita rastrear un objetivo. Si se considera un cuerpo rígido, asociado con tres vectores unitarios ortogonales fijados a su cuerpo (que representan los tres ejes del sistema de coordenadas locales del objeto). El problema básico es especificar la orientación de estos tres vectores unitarios, y por lo tanto del cuerpo rígido, con respecto al sistema de coordenadas del observador, considerado como una ubicación de referencia en el espacio.una ubicación de referencia en el espacio.
, 在幾何學中，三維空間中的旋轉具有多種表述，其將旋轉作為一種數學轉換處理。在物理學中， … 在幾何學中，三維空間中的旋轉具有多種表述，其將旋轉作為一種數學轉換處理。在物理學中，此概念被應用到古典力學，其中轉動運動學或角運動學為對旋轉運動的量化科學。一物體在某瞬間的定向透過同種工具描述。 根據歐拉旋轉定理，剛體（或有固定原點的三維座標系）的任意旋轉可透過對一些軸做幾次簡單旋轉來表述。這樣的旋轉最小有三個實參數來唯一描述。然而，因為各種不同的因素，實際上有數種表示法；其中不少表示法用了超過三個參數來描述，儘管自由度仍只有三個。 旋轉表示的一個例子為電腦視覺。在這例子中，自動化觀察者需要追蹤目標。考慮一剛體，其有三個正交單位向量固定在其主體上（代表該物體自身卡氏座標的三個軸）。其中基礎問題為如何訂出三個單位向量的定向，因此相對於觀察者座標系，剛體被認為是參考的空間定位。題為如何訂出三個單位向量的定向，因此相對於觀察者座標系，剛體被認為是參考的空間定位。
|
| http://dbpedia.org/ontology/thumbnail
|
http://commons.wikimedia.org/wiki/Special:FilePath/Euler_AxisAngle.png?width=300 +
|
| http://dbpedia.org/ontology/wikiPageExternalLink
|
http://rdcu.be/wIBC%7Cdoi-access=free +
, http://www.starlino.com/dcm_tutorial.html +
, http://www.euclideanspace.com/maths/geometry/rotations/index.htm +
, http://mathworld.wolfram.com/Cayley-KleinParameters.html +
, https://archive.org/details/mechanics00land +
, http://mesh.brown.edu/rotations +
, https://digitalrepository.unm.edu/math_fsp/4/ +
, http://www.mrao.cam.ac.uk/~clifford/introduction/intro/node9.html%23SECTION00030000000000000000 +
, https://web.archive.org/web/20190925150540/http:/www.malcolmdshuster.com/Pub_1993h_J_Repsurv_scan.pdf +
, http://www.malcolmdshuster.com/Pub_1993h_J_Repsurv_scan.pdf +
, http://www.j3d.org/matrix_faq/matrfaq_latest.html%23Q36 +
, https://semanticscholar.org/paper/932b4eaa22afb4384815db12dfd197c24c7ba355 +
, http://www.j3d.org/matrix_faq/matrfaq_latest.html%23Q37 +
|
| http://dbpedia.org/ontology/wikiPageID
|
7290730
|
| http://dbpedia.org/ontology/wikiPageLength
|
68869
|
| http://dbpedia.org/ontology/wikiPageRevisionID
|
1081069187
|
| http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Right-hand_rule +
, http://dbpedia.org/resource/Orthogonal_matrix +
, http://dbpedia.org/resource/Category:Euclidean_symmetries +
, http://dbpedia.org/resource/Quantity +
, http://dbpedia.org/resource/Rotation_matrix +
, http://dbpedia.org/resource/Rigid_body +
, http://dbpedia.org/resource/Time_derivative +
, http://dbpedia.org/resource/Hypercomplex_number +
, http://dbpedia.org/resource/Orthonormal_basis +
, http://dbpedia.org/resource/Dot_product +
, http://dbpedia.org/resource/Axis%E2%80%93angle_representation +
, http://dbpedia.org/resource/Orientation_%28geometry%29 +
, http://dbpedia.org/resource/Exterior_algebra +
, http://dbpedia.org/resource/Rotation_around_a_fixed_axis +
, http://dbpedia.org/resource/Vector_space +
, http://dbpedia.org/resource/Scalar_%28mathematics%29 +
, http://dbpedia.org/resource/Banked_turn +
, http://dbpedia.org/resource/Geometry +
, http://dbpedia.org/resource/Computer_vision +
, http://dbpedia.org/resource/Linear_map +
, http://dbpedia.org/resource/Identity_matrix +
, http://dbpedia.org/resource/Dimension_%28vector_space%29 +
, http://dbpedia.org/resource/Pergamon_Press +
, http://dbpedia.org/resource/Degrees_of_freedom_%28mechanics%29 +
, http://dbpedia.org/resource/Coordinate_system +
, http://dbpedia.org/resource/Pitching_moment +
, http://dbpedia.org/resource/Commutativity +
, http://dbpedia.org/resource/Unit_vector +
, http://dbpedia.org/resource/Aviation +
, http://dbpedia.org/resource/Real_number +
, http://dbpedia.org/resource/Plane_of_rotation +
, http://dbpedia.org/resource/Velocity_vector +
, http://dbpedia.org/resource/Stabilizer_%28group_theory%29 +
, http://dbpedia.org/resource/Active_and_passive_transformation +
, http://dbpedia.org/resource/Nutation +
, http://dbpedia.org/resource/Euclidean_space +
, http://dbpedia.org/resource/Elevation_%28ballistics%29 +
, http://dbpedia.org/resource/Trigonometric_function +
, http://dbpedia.org/resource/Category:Orientation_%28geometry%29 +
, http://dbpedia.org/resource/Center-of-mass_frame +
, http://dbpedia.org/resource/Rodrigues%27_rotation_formula +
, http://dbpedia.org/resource/Gimbal_lock +
, http://dbpedia.org/resource/Euler_filter +
, http://dbpedia.org/resource/Transformation_%28geometry%29 +
, http://dbpedia.org/resource/Atan2 +
, http://dbpedia.org/resource/Quaternion +
, http://dbpedia.org/resource/Trace_%28linear_algebra%29 +
, http://dbpedia.org/resource/Kinematics +
, http://dbpedia.org/resource/Real_coordinate_space +
, http://dbpedia.org/resource/Yaw_%28rotation%29 +
, http://dbpedia.org/resource/Rotation_%28mathematics%29 +
, http://dbpedia.org/resource/Point_%28geometry%29 +
, http://dbpedia.org/resource/Rotation +
, http://dbpedia.org/resource/Course_%28navigation%29 +
, http://dbpedia.org/resource/Motion_%28physics%29 +
, http://dbpedia.org/resource/Category:Rigid_bodies_mechanics +
, http://dbpedia.org/resource/Round-off_error +
, http://dbpedia.org/resource/Category:Rotation_in_three_dimensions +
, http://dbpedia.org/resource/Joint_%28mechanics%29 +
, http://dbpedia.org/resource/Affine_space +
, http://dbpedia.org/resource/Determinant +
, http://dbpedia.org/resource/Three-dimensional_rotation_operator +
, http://dbpedia.org/resource/Stereographic_projection +
, http://dbpedia.org/resource/Pauli_matrices +
, http://dbpedia.org/resource/D._Reidel +
, http://dbpedia.org/resource/Eigenvector +
, http://dbpedia.org/resource/Imaginary_unit +
, http://dbpedia.org/resource/Power_series +
, http://dbpedia.org/resource/Versor +
, http://dbpedia.org/resource/Classification_of_discontinuities +
, http://dbpedia.org/resource/Basis_%28linear_algebra%29 +
, http://dbpedia.org/resource/Translation_%28geometry%29 +
, http://dbpedia.org/resource/Quaternions_and_spatial_rotation +
, http://dbpedia.org/resource/File:Praezession.svg +
, http://dbpedia.org/resource/Gnomonic_projection +
, http://dbpedia.org/resource/Cross_product +
, http://dbpedia.org/resource/Function_composition +
, http://dbpedia.org/resource/Euler_angles +
, http://dbpedia.org/resource/Category:Rotation +
, http://dbpedia.org/resource/Automation +
, http://dbpedia.org/resource/Transitive_relation +
, http://dbpedia.org/resource/Classical_mechanics +
, http://dbpedia.org/resource/Complex_numbers +
, http://dbpedia.org/resource/Orientation_%28vector_space%29 +
, http://dbpedia.org/resource/Origin_%28mathematics%29 +
, http://dbpedia.org/resource/Eigenvalues +
, http://dbpedia.org/resource/File:Euler_AxisAngle.png +
, http://dbpedia.org/resource/Euler%27s_rotation_theorem +
, http://dbpedia.org/resource/Geometric_algebra +
, http://dbpedia.org/resource/Circular_motion +
, http://dbpedia.org/resource/Lie_product_formula +
, http://dbpedia.org/resource/Precession +
, http://dbpedia.org/resource/Gyroscope +
, http://dbpedia.org/resource/Multivector +
, http://dbpedia.org/resource/Cartesian_coordinate_system +
, http://dbpedia.org/resource/Bivector +
, http://dbpedia.org/resource/Inner_product +
|
| http://dbpedia.org/property/bgcolor
|
#FAFFFB
|
| http://dbpedia.org/property/borderColour
|
#0070BF
|
| http://dbpedia.org/property/cellpadding
|
6
|
| http://dbpedia.org/property/indent
|
:
|
| http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Short_description +
, http://dbpedia.org/resource/Template:Sfrac +
, http://dbpedia.org/resource/Template:Pi +
, http://dbpedia.org/resource/Template:Equation_box_1 +
, http://dbpedia.org/resource/Template:Commons_category +
, http://dbpedia.org/resource/Template:Refend +
, http://dbpedia.org/resource/Template:Refbegin +
, http://dbpedia.org/resource/Template:Math +
, http://dbpedia.org/resource/Template:Main +
, http://dbpedia.org/resource/Template:Broader +
, http://dbpedia.org/resource/Template:Reflist +
, http://dbpedia.org/resource/Template:See_also +
, http://dbpedia.org/resource/Template:Main_article +
, http://dbpedia.org/resource/Template:Cite_journal +
, http://dbpedia.org/resource/Template:Cite_book +
, http://dbpedia.org/resource/Template:Mvar +
|
| http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Rotation +
, http://dbpedia.org/resource/Category:Rotation_in_three_dimensions +
, http://dbpedia.org/resource/Category:Rigid_bodies_mechanics +
, http://dbpedia.org/resource/Category:Orientation_%28geometry%29 +
, http://dbpedia.org/resource/Category:Euclidean_symmetries +
|
| http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions?oldid=1081069187&ns=0 +
|
| http://xmlns.com/foaf/0.1/depiction
|
http://commons.wikimedia.org/wiki/Special:FilePath/Praezession.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Euler_AxisAngle.png +
|
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions +
|
| owl:sameAs |
http://fa.dbpedia.org/resource/%D8%B1%D9%88%D8%B4%E2%80%8C%D9%87%D8%A7%DB%8C_%D9%85%D8%AF%D9%84_%DA%A9%D8%B1%D8%AF%D9%86_%DA%86%D8%B1%D8%AE%D8%B4_%D8%AF%D8%B1_%D8%B3%D9%87_%D8%A8%D8%B9%D8%AF +
, http://es.dbpedia.org/resource/Formalizaci%C3%B3n_de_la_rotaci%C3%B3n_en_tres_dimensiones +
, http://rdf.freebase.com/ns/m.025yc06 +
, http://www.wikidata.org/entity/Q7370306 +
, https://global.dbpedia.org/id/4uf8W +
, http://zh.dbpedia.org/resource/%E4%B8%89%E7%B6%AD%E7%A9%BA%E9%96%93%E7%9A%84%E6%97%8B%E8%BD%89%E8%A1%A8%E8%BF%B0 +
, http://dbpedia.org/resource/Rotation_formalisms_in_three_dimensions +
, http://yago-knowledge.org/resource/Rotation_formalisms_in_three_dimensions +
|
| rdf:type |
http://dbpedia.org/class/yago/SpatialProperty105062748 +
, http://dbpedia.org/class/yago/Symmetry105064827 +
, http://dbpedia.org/class/yago/Attribute100024264 +
, http://dbpedia.org/class/yago/Abstraction100002137 +
, http://dbpedia.org/class/yago/Property104916342 +
, http://dbpedia.org/class/yago/WikicatEuclideanSymmetries +
|
| rdfs:comment |
在幾何學中，三維空間中的旋轉具有多種表述，其將旋轉作為一種數學轉換處理。在物理學中， … 在幾何學中，三維空間中的旋轉具有多種表述，其將旋轉作為一種數學轉換處理。在物理學中，此概念被應用到古典力學，其中轉動運動學或角運動學為對旋轉運動的量化科學。一物體在某瞬間的定向透過同種工具描述。 根據歐拉旋轉定理，剛體（或有固定原點的三維座標系）的任意旋轉可透過對一些軸做幾次簡單旋轉來表述。這樣的旋轉最小有三個實參數來唯一描述。然而，因為各種不同的因素，實際上有數種表示法；其中不少表示法用了超過三個參數來描述，儘管自由度仍只有三個。 旋轉表示的一個例子為電腦視覺。在這例子中，自動化觀察者需要追蹤目標。考慮一剛體，其有三個正交單位向量固定在其主體上（代表該物體自身卡氏座標的三個軸）。其中基礎問題為如何訂出三個單位向量的定向，因此相對於觀察者座標系，剛體被認為是參考的空間定位。題為如何訂出三個單位向量的定向，因此相對於觀察者座標系，剛體被認為是參考的空間定位。
, En geometría, existen varias formalizacion … En geometría, existen varias formalizaciones para expresar una rotación en tres dimensiones como una matemática. En física, este concepto se aplica a la mecánica clásica, donde la cinemática rotacional (o angular) es la ciencia que describe cuantitativamente un movimiento puramente rotativo. La orientación de un objeto en un instante dado se describe con las mismas herramientas, ya que se define como una rotación imaginaria a partir de una ubicación de referencia en el espacio, en lugar de una rotación realmente observada de una ubicación anterior en el espacio.a de una ubicación anterior en el espacio.
, In geometry, various formalisms exist to e … In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space.tation from a previous placement in space.
|
| rdfs:label |
Rotation formalisms in three dimensions
, Formalización de la rotación en tres dimensiones
, 三維空間的旋轉表述
|
| rdfs:seeAlso |
http://dbpedia.org/resource/4-dimensional_Euclidean_space +
, http://dbpedia.org/resource/Rotations +
, http://dbpedia.org/resource/Angle +
, http://dbpedia.org/resource/Rodrigues%27_rotation_formula +
, http://dbpedia.org/resource/Rotation_matrix +
|
