Coordinate rotation switching method based on three angles and two positions

Abstract

The invention provides a coordinate rotation switching method based on three angles and two positions. A mode of deviation and then rotation or a mode of rotation and then deviation is adopted, and rotation switching between any two right-angle coordinate systems in space can be achieved; one of the two coordinate systems is regarded as an initial coordinate system, and the other one is regarded as an end coordinate system; by introducing the concept of deviation vector axis and deviation vector angle, according to the state of the initial coordinate system and the state of the end coordinate system, according to the fixed steps, three parameters including deviation vector angle, deviation rotation angle and rotation angle of three angles can be rapidly determined, and therefore a corresponding rotation matrix can be obtained. Compared with a traditional rotation coordinate system switching method based on quaternions and eulerian angles, the method is more visual and simpler on the aspect of specific value determining of the parameters; compared with a three-time rotation method of eulerian angle rotation switching, a three-angle two-position rotation mode put forward in the method is simpler and more convenient on the aspects of form and content. The method belongs to the field of coordinate rotation switching and can be applied to rotation switching of any two coordinate systems in space.

Description

technical field [0001] The invention relates to a rotation coordinate transformation method based on ternary angle and two positions, which is suitable for rotation transformation between any rectangular coordinate systems in space, and can be widely used in the fields of modulation and demodulation, attitude control, three-dimensional animation design and the like. technical background [0002] Attitude transformation plays an important role in satellite attitude adjustment, robot and manipulator operation, 3D animation production, navigation guidance and other fields. For the convenience of mathematical analysis, the commonly used attitude transformation description methods are Euler angles and quaternions. [0003] Euler rotation follows a certain sequence of coordinate axes (such as X-axis first, then Y-axis, and finally Z-axis), and each axis rotates by a certain angle. After three rotations, the transformation of any two coordinate systems in space can be realized. Wh...

AI Technical Summary

Problems solved by technology

[0009] The technical problem of the present invention is: Aiming at the problem that the Euler rotation and the quaternion rotation cannot conveniently describe the compound rotation motion and the required parameters cannot be conveniently found according to the initial and final states of the coordinate system, a new rotation method with two positions of ternary angle is proposed. method, through first deflection and then rotation or first rotation and then deflection two transpositions, any two rectangular coordinate systems in space can be coincident; according to the state of the initial and final coordinate systems, it is convenient to find out the required The specific position of the parameter content; at the same time, it can also conveniently express the rotation matrix of the compound rotation motion, which provides a new technical approach for the rotation representation method of the coordinate system

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