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8-Gravel

## Calculate the Theat for a invers quartic potential

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

1 ACCEPTED SOLUTION

Accepted Solutions
23-Emerald III
(To:WalterSchrabmai)

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

13 REPLIES 13

Hi,

Enclosed are functions.  Is this what you want?

Cheers

Terry

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

I can not do it.

What Could I do?

best

23-Emerald III
(To:WalterSchrabmai)

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

8-Gravel
(To:LucMeekes)
Great! Thanks a lot!
Best regards
Walter
8-Gravel
(To:LucMeekes)

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

23-Emerald III
(To:WalterSchrabmai)

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

8-Gravel
(To:LucMeekes)

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.

23-Emerald III
(To:WalterSchrabmai)

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

8-Gravel
(To:LucMeekes)

Awesome! Great! Thanks a lot.

Hi

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

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

8-Gravel
(To:AlanStevens)

Thanks a lot!

8-Gravel
(To:LucMeekes)

Great!

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