旋转矩阵-欧拉角.docxVIP

1.来自wikipedia：/wiki/Tait-Bryan_angles#Tait.E2.80.93Bryan_anglesEuler anglesFrom Wikipedia, the free encyclopedia(Redirected from Tait-Bryan angles)Jump to: navigation, searchThis article is about the Euler angles used in mathematics. For the use of the term in aerospace engineering, see flight dynamics.The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body.[1] To describe such an orientation in 3-dimensionalEuclidean 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 also represent three composed rotations that move a reference frame to a given referred frame. This is equivalent to saying that any orientation can be achieved by composing three elemental rotations (rotations around a single axis), and also equivalent to saying that any rotation matrix can be decomposed as a product of three elemental rotation matrices.Without considering the possibilities of different signs for the angles or moving the reference frame, there are twelve different conventions divided in two groups. One of them is called proper Euler angles and the other Tait–Bryan angles. Sometimes Euler angles is used for all of them.Contents[hide] 1 Proper Euler Angles1.1 Classic definition1.2 Angles signs and ranges1.3 Angles of a given frame. Geometric derivation.1.4 Conventions for proper Euler angles2 Tait–Bryan angles2.1 Double naming problem3 Relationship with physical motions3.1 Euler angles as composition of intrinsic rotations3.2 Euler angles as composition of extrinsic rotations3.3 Euler rotations3.3.1 Gimbal analogy3.3.2 Intermediate frames4 Relationship to other representations4.1 Matrix orientation4.2 Quaternions4.3 Geometric algebra5 Properties6 Higher dimensions7 Applications7.1 Vehicles and moving frames7.2 Others8 See also9 References10 Bibliography11 External links[edit] Proper Euler AnglesEuler angles – The xyz (fixed) system is shown