 My Math Forum How to find the rotation vector by deriving the final vector with respect to the disp

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 April 18th, 2019, 12:10 PM #1 Newbie   Joined: Apr 2019 From: Pune Posts: 1 Thanks: 0 How to find the rotation vector by deriving the final vector with respect to the disp My understanding of a rotation of a vector can be done by using a 2D rotation matrix as shown below, $R(\theta )=\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \\\end{bmatrix}$. This rotates column vectors by means of the following matrix multiplication, $\begin{bmatrix}x'\\y'\end{bmatrix} = \begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \\\end{bmatrix}\begin{bmatrix}x\\y \end{bmatrix}$ For example, if you rotate the vector x=$\begin{bmatrix}1\\1 \end{bmatrix}$ by 45 degrees (clockwise), then the new vector is $\begin{bmatrix} \sqrt2 \\ 0 \end{bmatrix}$. **Other Method:** If I have only initial and final coordinates of the vectors [![enter image description here]] The initial vector is, V = $\begin{bmatrix}1\\1 \end{bmatrix}$ and the final vector is, v = V+d = $\begin{bmatrix} \sqrt2 \\ 0 \end{bmatrix}$. The displacement between these vectors is d = $\begin{bmatrix} \sqrt2-1 \\ -1 \end{bmatrix}$. Can I derive the final vector v with respect to displacement $\frac{\partial{v}}{\partial{d}}$ to get the rotation vector? [but returns a identity matrix] If so, does $\frac{\partial{v}}{\partial{d}} * d$ can be used to cross-check? : https://i.stack.imgur.com/hYDJn.png April 19th, 2019, 03:39 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,116 Thanks: 2331 How would $\frac{\partial v}{\partial d}$ be defined? Tags deriving, disp, final, find, respect, rotation, vector Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post henrymerrild Calculus 4 October 29th, 2014 12:39 AM Tiago Costa Algebra 2 August 18th, 2013 02:54 PM sainistar Linear Algebra 0 February 12th, 2012 05:57 PM babarorhum Algebra 0 October 20th, 2011 04:53 PM rfrank Algebra 0 July 31st, 2009 08:05 AM

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