正常转动和不正常转动理论中的第二正交性条件。轨迹方程和长期方程的解

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-07-01 DOI:10.6028/JRES.073B.021

H. Gelman

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引用次数: 2

摘要

基于旋转矩阵的群性质和周期性性质，用纯解析的方法求解了第二正交条件的直接结果——旋转矩阵的迹与其平方的迹的连接方程和旋转矩阵的长期方程。由此可见，众所周知的关于旋转矩阵的轨迹的转角和关于旋转矩阵本身的轴和转角的公式，都与旋转矩阵的代数性质密切相关。

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The second orthogonality conditions in the theory of proper and improper rotations.IV. Solution of the trace and secular equations

The equation which connects the trace of a rotation matrix and that of its square, and the secular equation for a rotation matrix , both of which are direct res ults of the second orthogonality conditions, are solved by purely analytic methods based on the group property and the periodicity property of rotation matrices. The point is thus made that the well known formulas for the trace of a rotation matrix in terms of the angle of rotation and for the rotation matrix itself in terms of the axis and angle of rotation, are closely related to the algebraic properties of rotation matrices.

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Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences

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