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I'm guessing AMM is going to do a theoretical project.

Another joyous vector calculus proof for you guys to assist me with! Our lovely tutor has set us some extra exam questions on vector calculus and I thought they were going well until I saw this one! HELP!!!

=====

Q. A soolid of uniform density occupies a volume V bounded by a surface S. Show that the z-component of its centre of mass,

Zo = (Integral z dV)/(Integral dV)

can be written in the alternative form:

Zo = (3 * Integral zr.dS)/(4 * Integral r.dS)

I'm guessing it's do with the divergence (or Gauss') theorem:

Integral DivA dV = Integral F.dS

and that we have to say z is equivalent to DivA...but I really have no idea how to proceed! any ideas?

Another joyous vector calculus proof for you guys to assist me with! Our lovely tutor has set us some extra exam questions on vector calculus and I thought they were going well until I saw this one! HELP!!!

=====

Q. A soolid of uniform density occupies a volume V bounded by a surface S. Show that the z-component of its centre of mass,

Zo = (Integral z dV)/(Integral dV)

can be written in the alternative form:

Zo = (3 * Integral zr.dS)/(4 * Integral r.dS)

I'm guessing it's do with the divergence (or Gauss') theorem:

Integral DivA dV = Integral F.dS

and that we have to say z is equivalent to DivA...but I really have no idea how to proceed! any ideas?

ANDDDDDDDDDDDDDDDDDDDD another vector calculus question:

======

Q. Calculate grad (a.r)^2

where r is the position vector and a is a constant vector

======

I wrote r=(x,y,z) and a=(a,b,c) and tried expanding it, but I get something horrible which doesn't appear to simplify!!! Ideas?!

*****

Can someone also confirm that I'm right in that curl{(a.r)a} = 0

======

Q. Calculate grad (a.r)^2

where r is the position vector and a is a constant vector

======

I wrote r=(x,y,z) and a=(a,b,c) and tried expanding it, but I get something horrible which doesn't appear to simplify!!! Ideas?!

*****

Can someone also confirm that I'm right in that curl{(a.r)a} = 0

Bezza

You can just use the chain rule can't you

Unparseable latex formula:

then the other bits are just times b and c so you get \fontsize{5}\frac{\partial}{\partial x}(ax+by+cz)^2 = 2(ax+by+cz)\times a

Unparseable latex formula:

\fontsize{5}\nabla (\bf{a}.\bf{r})^2 = 2(\bf{a}.\bf{r})\bf{a}

Ooooo that sounds like a nifty way of doing it! Thanks I'll have a go a bit later (now onto circuit theory!).

Just for your interest, thought I might put up the formal proof of that....(OK, I admit it I like using the crazy suffix ****....)

EDIT: What the frig? It automatically stars things?

EDIT: What the frig? It automatically stars things?

Worzo

Just for your interest, thought I might put up the formal proof of that....(OK, I admit it I like using the crazy suffix ****....)

EDIT: What the frig? It automatically stars things?

EDIT: What the frig? It automatically stars things?

You're not allowed to swear andy, tut tut And you are SERIOUSLY obsessed with Einstein's Summation principle...but then again, I do agree that it is v.cool (I MUST teach myself it!)

Y'know, it's not all Einstein's work. All he did was to decide to remove the sigma sign when you repeat an index twice. He didn't think of using the suffix notation in the first place. That question was a perfect example for it really. All Bezza did was say, "do this for the x-component, and then look, it's the same for the rest". The suffix notation puts the "look, it's the same for the rest" into a handy generalisation.

EDIT: Not allowed to swear? What a load of sh|tty b0||0cks.

EDIT: Not allowed to swear? What a load of sh|tty b0||0cks.

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