Content deleted Content added
Citation bot (talk | contribs) Add: s2cid, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Whoop whoop pull up | #UCB_webform 2/64 |
→Representing rigid body motions: small correction with half x and y in a translational q, and also add conventional deltas to indicate change in x and y |
||
Line 80:
# When <math>B \neq 0</math>, the element <math>q</math> can be written as <math display="block">\cos(\theta/2) + \sin(\theta/2)(i + x\varepsilon j + y\varepsilon k),</math> which denotes a rotation of angle <math>\theta</math> around the point <math>(x,y)</math>.
# When <math>B = 0</math>, the element <math>q</math> can be written as <math display="block">\begin{aligned}&1 + i\left(\frac{\Delta x}{2} \varepsilon j + \frac{\Delta y}{2}\varepsilon k\right)\\ = {} & 1 - \frac{\Delta y}{2}\varepsilon j + \frac{\Delta x}{2}\varepsilon k,\end{aligned}</math> which denotes a translation by vector <math>\begin{pmatrix}\Delta x \\ \Delta y\end{pmatrix}.</math>
== Geometric construction ==
| |||