Thread: Old man needs help with rusty maths

Hi Guys

been about 20years since i felexed my maths muscle and it apears to have weakened somewhat.


Im reading a research paper and going through the equations therein and have come across a part I cant solve.

I dont want to just use the papers equations without understanding how they were derived (not my style) so any help with this bottleneck would be really appreciated

Heres what the paper gives:


V = wA/2Nr


where V is a radial velocity hence can be rewrited as = -dr/dt (where r is radial position and t is time)


We need to solve for r.


the paper gives the initial condition, r=ro at t=0 (where ro is a constant)



It then gives a solution for r as:- r= (ro^2- (wAt/N)^0.5


I cant see how they get that.....

can anyone shed any light on this?



I assumed I just needed to substitute ro and integrate with respect to t

giving r = wAt/2Nro?


but thats not what the paper is showing.


I can only assume im missing something/forgotten something. any help would be appreciated

Originally Posted by mgadd

Hi Guys

been about 20years since i felexed my maths muscle and it apears to have weakened somewhat.


Im reading a research paper and going through the equations therein and have come across a part I cant solve.

I dont want to just use the papers equations without understanding how they were derived (not my style) so any help with this bottleneck would be really appreciated

Heres what the paper gives:


V = wA/2Nr


where V is a radial velocity hence can be rewrited as = -dr/dt (where r is radial position and t is time)


We need to solve for r.


the paper gives the initial condition, r=ro at t=0 (where ro is a constant)



It then gives a solution for r as:- r= (ro^2- (wAt/N)^0.5


I cant see how they get that.....

can anyone shed any light on this?



I assumed I just needed to substitute ro and integrate with respect to t

giving r = wAt/2Nro?


but thats not what the paper is showing.


I can only assume im missing something/forgotten something. any help would be appreciated

the key in solving this ODE is that in can be rewritten by means of separation of variables

Shouldn't that be 2r nought squared under the radical?

Originally Posted by Ledger

Shouldn't that be 2r nought squared under the radical?

yup it should, think Dr.Rocket forgot to write it.

Originally Posted by Ledger

Shouldn't that be 2r nought squared under the radical?

yup it should, think Dr.Rocket forgot to write it. Wait, actually it shouldnt, the constant should be (-r_0^2)/2 not -r_0^2