Spatial Axes
Let events in the history of some particle be described by their phase angle $\theta$. And recall that the vectors $\hat{m} \equiv (1, 0, 0)$, $\hat{e} \equiv (0, 1, 0)$ and $\hat{z} \equiv (0, 0, 1)$ mark the magnetic, electric and polar axes. These algebraic entities can be used to construct another set of vectors. Definition: the axis of the abscissa is composed from all scalar multiples of
$\hat{x} \equiv \cos{\! 2\theta} \, \hat{m} + \sin{\! 2\theta} \, \hat{e}$
And similarily the ordinate axis is defined by
$\hat{y} \equiv - \sin{\! 2\theta} \, \hat{m} + \cos{\! 2\theta} \, \hat{e}$
These new vectors together with $\hat{z}$ are called a Cartesian basis after the work of René Descartes
Related WikiMechanics articles.
page revision: 112, last edited: 01 Oct 2021 16:54