引用本文: 张媛, 王士敏, 王琪. 对定点运动刚体欧拉角的独立性及坐标变换矩阵的分析[J]. 力学与实践, 2022, 44(2): 385-389.
ZHANG Yuan, WANG Shimin, WANG Qi. ANALYSIS ON THE INDEPENDENCE OF EULER ANGLES AND THE COORDINATE TRANSFORMATION MATRIX[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 385-389.
 Citation: ZHANG Yuan, WANG Shimin, WANG Qi. ANALYSIS ON THE INDEPENDENCE OF EULER ANGLES AND THE COORDINATE TRANSFORMATION MATRIX[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 385-389.

## ANALYSIS ON THE INDEPENDENCE OF EULER ANGLES AND THE COORDINATE TRANSFORMATION MATRIX

• 摘要: 讨论了欧拉角的独立性以及构造随体坐标到固定坐标系变换矩阵时的三次转动顺序问题,引入中间坐标系的概念,说明了将有限位移视为三次转动时,与欧拉角所对应的转动与转动顺序无关,但是,在所有可能的转动顺序中,存在一个顺序,使得每次转动都是绕着两个坐标系的共同坐标轴进行的,由于这样的变换关系最为简单,因此,通常选择用这个顺序来构建随体坐标到固定坐标系变换矩阵。

Abstract: The independence of the Eulerian Angles and the rotation sequence in constructing of transformation matrix from body coordinates to fixed coordinate problems are discussed in this paper, by introducing the transition coordinate system. The rigid body position is independent of the rotation sequence corresponding to Eulerian angles. However, there exists a sequence in all of them, in which each of the three rotations is carried out around common coordinate axes of the two coordinate systems associated with each other, and the transformation relation of each rotation is expressed with simple transformation for rotation about a fixed axis. Therefore, this sequence is chosen to construct the transformation matrix from the body coordinate to the fixed coordinate system.

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