“rotation”的概念、定义、习题解题方法及翻译-数学辞典

单词

rotation

释义

rotation

A rotation of the plane about the origin O through an angle α is the transformation of the plane in which O is mapped to itself, and a point P with polar coordinates (r,θ) is mapped to the point P′ with polar coordinates (r,θ + α). In terms of Cartesian coordinates, P with coordinates (x,y) is mapped to P′ with coordinates (x′,y′), where

Rotation about O by α

This change of coordinates can be represented by the matrix equation

Importantly, distances and angles are still calculated the same using x᾽ and y᾽ as when using x and y. Note that the matrix is orthogonal and has determinant 1. In 3-dimensional space, an orthogonal matrix with determinant 1 represents a rotation about an axis through the origin.

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