“rotation”的概念、定义、翻译、参考文献-科学参考

rotation

Mathematics

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

$\begin{array}{l} x' = x cos α - y sin α, \\ y' = x sin α + y cos α . \end{array}$

Rotation about O by α‎

This change of coordinates can be represented by the matrix equation

$(\begin{matrix} x' \\ y' \end{matrix}) = (\begin{matrix} cos α & - sin α \\ sin α & cos α \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) .$

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.

Astronomy

The turning of a body on its axis, such as the daily rotation of the Earth. It is usually measured relative to the stars, and termed the sidereal period of axial rotation.

单词	rotation
释义	rotation Mathematics 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 $\begin{array}{l} x' = x cos α - y sin α, \\ y' = x sin α + y cos α . \end{array}$ Rotation about O by α‎ This change of coordinates can be represented by the matrix equation $(\begin{matrix} x' \\ y' \end{matrix}) = (\begin{matrix} cos α & - sin α \\ sin α & cos α \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) .$ 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. Astronomy The turning of a body on its axis, such as the daily rotation of the Earth. It is usually measured relative to the stars, and termed the sidereal period of axial rotation.
随便看	acute angle acute-phase response ACV acyclic acyclic graph acyclovir acyl anhydrides acylation acyl fission acylglycerols acyl group acyl halides Ada Ada 95 AdaBoost Adam adamantane adamantine adamellite Adams catalyst Adams, John (1735–1826) Adams, John Couch Adams, John Couch (1819–92) Adams, John Quincy (1767–1848) Adams methods