Recent content by peterspencers

Yes this gives the required result, thankyou very much for taking the time to point out my mistake. Kind regards, Peter

ok, so the acceleration should just be ##-g\textit{k}##?

Hi there, I have edited the initial post, apologies, I had put the unit vectors j and k in the wrong place, thankyou for correcting me. I have also included an extra line showing where the acceleration vector comes from, it is simply the second derivative of position with respect to phi + the...

Homework Statement The following question involves a torque acting on a particle in rotational motion. It provides practice with the various equations for angular velocity, torque etc A particle of mass ##m## initially has position...

Ok, let me just get a few things cleared up in my understanding.. Firstly, the questions I am attempting to solve are on Einstein summation convention, so the question should be written.. $$\sum_{j=1}^{3} x_{j}b_{ij} = x^{j}b^{i}_{j}$$ Which means that the sum is equal to ...

Ok, I think I understand, many thanks for your patient help. Just to make sure I've understood correctly, if we take another example: $$\sum_{j=1}^{3} x_{j}b_{ij}$$ This would then equal.. $$x_{1}b_{i1}+x_{2}b_{i2}+x_{3}b_{i3}$$ Which is the dot product of the matrices...

so, just to make sure I am with you so far, the entry position of ##(A \cdot x)_{i}## $$=\sum_{j=1}^{n} a_{ij}x_{j}$$ Where ##j## represents columns in the matrix ##A## and rows in the matrix ##x## and $$(A \cdot x)=Ax$$ where A is a square matrix ...

$$(AB)_{ik}=\begin{pmatrix}a_{11}b_{11}+a_{12}b_{21}&a_{11}b_{12}+a_{12}b_{22}\\a_{21}b_{11}+a_{22}b_{21}&a_{21}b_{12}+a_{22}b_{22}\end{pmatrix}$$ and $$(A(\cdot)x)_{i}=a_{i1}x_{1}+a_{i2}x_{2}+... a_{in}x_{n}$$ May I ask what the correct latex code for A dot x is?

For the first task. $$ \begin{bmatrix}a_{ij}&a_{ij}&a_{ij}\end{bmatrix}\cdot\begin{bmatrix}b_{jk}\\b_{jk}\\b_{jk}\end{bmatrix}$$ And for the second tast...

To write the original question in Einstein summation, it would be.. ? $$a_{ij}b_{jk}x_{k}$$ for (i,k) = (2,3) we get.. ? $$a_{2j}b_{j3} = a_{21}b_{13}+a_{22}b_{23}+a_{23}b_{33}$$ And in the ith row and kth column we would have... ? $$a_{i1}b_{1k}+a_{i2}b_{2k}+a_{i3}b_{3k}$$

So, the inner sum has one repeated indicie and two free indices, so therefore has nine equations, forming a 3x3 matrix with three terms in each equation, giving us... $$...

Homework Statement The question asks us to write down the matrix represented by the following summation. 2. Homework Equations The question summation... $$\sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k}$$ The Attempt at a Solution $$ \sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k} =...

Homework Statement Hi there, I am attempting to prove a trigonometric equation using the half angle and double angle formulae Homework Equations See image one... The Attempt at a Solution See image two... I get stuck after the second line and can't see how to continue, please help.[/B]

I couldn't see that all you needed to do was factor out the 1/R as x

your right I am completely wrong, I took the same exam today, luckily I realized before I answered the question.