Calculate the Theat for a invers quartic potential

[WalterSchrabmai]

HI friends,

I am looking to get the solution for a Tetha for a quatrics potential from these equations:

(Reference: Classical Mechanics by Herbert Goldstein 1980 2nd ed.)

I have a potential  

V(r) = const / r^4.

Can anyone here help me with a MathCAD 15 Sheet, how to do it?

Thanks

Walter

[terryhendicott]

Hi,

Enclosed are functions.  Is this what you want?

Cheers

Terry

[WalterSchrabmai]

Thanks a lot, but I need a symbolically solution for that.

I can not do it.

What Could I do?

best

[LucMeekes · Accepted solution]

It's not completely impossible:

But then there is WolframAlpha:

Now the biggest hurdle may be to have Mathcad calculate the function F, the elliptic integral of the first kind...

Success!
Luc

[WalterSchrabmai]

Great! Thanks a lot!
Best regards
Walter

[WalterSchrabmai]

I have found this sheet for elliptic integrals....but its MMA! Never kind, thanks a lot.

http://functions.wolfram.com/EllipticIntegrals/EllipticK/introductions/CompleteEllipticIntegrals/ShowAll.html

[LucMeekes]

You mean 'Mixed Mathematical Arts'?

It's not that bad. In Mathcad 11 its available in the symbolic processor (Maple):

Do you happen to have a set of numerical values for E, l, m and R ?

I might be able to get you a plot of Theta versus r

Luc

[WalterSchrabmai]

Thanks Luc,

I have realized that the limits must be chosen carefully to get a real theta angle.

Although the analytical solution is fine, it could be done also numerically.

[LucMeekes]

Certainly, that's possible.

Be careful to choose your parameter values then, and inspect the integrand before the numerical integration. In your case, no wonder you got an imaginary result:

I had to move the values quite substantially to allow r to go/start near 0:

Success!
Luc

[WalterSchrabmai]

Awesome! Great! Thanks a lot.

[WalterSchrabmai]

Hi

Can anyone here tell me why in teh free SMath Studio there is a other/wrong solution?

[AlanStevens]

The upper limit on your inset diagram is e not b.  If you change b in SMath to 0.11 you get 0.007 (to three decimal places).  

Alan

[WalterSchrabmai]

Thanks a lot!

[WalterSchrabmai]

Great!