Solved: asymptote + odesolve

ValeryOchkov · ‎Jan 03, 2016

Is there a way to find an asymptote of a function created by the Odesolve function

LucMeekes · ‎Jan 06, 2016

Thank you.

I think it's a great honour to be named second in place after Christiaan Huygens.

Luc

View solution in original post

LucMeekes · ‎Jan 03, 2016

Hi Valery,

The right-sided asymptote is:

Provided you make sure that F is the point on the y-axis where your focus lies.

In your case F would be -10 (mm).

To get a two-sided asymptote, just replace x with sqrt(x^2).

This plot was made with dimensionless numbers, F= -3, n= sqrt(2).

Regards,

Luc

ValeryOchkov · ‎Jan 03, 2016

Thanks, Luc.

Happy NY!

But I think about the red function, not black.

Val

LucMeekes · ‎Jan 04, 2016

Hi Valery,

The asymptote I gave IS about the y1 function, not the y2....

Note that for the black function, the asymptote goes through (0,-10mm), whereas the y1 asymptote goes through (0,-10/3) for your values of F=1 cm=10 mm and n=2 according to the function I provided: F/ (n+ 1)= -10/ 3.

Luc

ValeryOchkov · ‎Jan 04, 2016

LucMeekes написал(а):

Hi Valery,

The asymptote I gave IS about the y1 function, not the y2....

Luc

And what is an analytical view of this function?

LucMeekes · ‎Jan 04, 2016

Ok Valery, here it comes:

Well you know how to solve it numerically, using Odesolve.

I give you the symbolic solution:

An example with F= -1, n=sqrt(2):

To find the asymptote:

Regards,

Luc

ValeryOchkov · ‎Jan 05, 2016

Thanks, Luc!

Now I know two man from NL

Christiaan Huygens - Wikipedia
Luc Meekes

LucMeekes · ‎Jan 06, 2016

Thank you.

I think it's a great honour to be named second in place after Christiaan Huygens.

Luc

ValeryOchkov · ‎Feb 29, 2016

LucMeekes написал(а):

Thank you.

I think it's a great honour to be named second in place after Christiaan Huygens.

Luc

About it in my article - http://twt.mpei.ac.ru/ochkov/Mirror-Lens-macket.pdf

ValeryOchkov · ‎Jan 06, 2016

And what is the formula for y(x, F, n) at the case not n=sin a/sin b - for n=a/b?

LucMeekes · ‎Jan 06, 2016

Is this a physical reality?

ValeryOchkov · ‎Jan 06, 2016

LucMeekes написал(а):

Is this a physical reality?

At little angles! See plots avove!

This is a solution of one DE!

RichardJ · ‎Jan 06, 2016

Hi Luc

Could you post the worksheet for that?

Thanks.

VladimirN · ‎Jan 06, 2016

I join the request too.

LucMeekes · ‎Jan 06, 2016

Hi Rich,

Here you are.

It's Mathcad 11. I suspect some things will not work in other versions.

Luc

RichardJ · ‎Jan 06, 2016

Thanks.

You are correct. A lot of the symbolic stuff does not work with the Mupad engine. If I find the time I'll see if I can fix it.

ValeryOchkov · ‎Jan 07, 2016

From my future article - sorry - Google translation:

We used two methods for solving optical problems - numerically using Mathcad-function Odesolve and analytical through the site wolfralpha.com. But there is a third (crafty and lazy) way of solving such problems. You can place a problem on the site PTC Community/Mathcad and wait for it someone decides. Thus it was obtained "terrible" formula for y1s (x), placed in the center of the figure 7. It is calculated profile of the focusing lens without changing their angles of the sinuses. This formula (complex analytic solution of a differential equation) led one user Mathcad from Holland - the birthplace of the great Christian Huygens, who made a great contribution to the development of optics - see. https://community.ptc.com/t5/PTC-Mathcad/asymptote-odesolve/td-p/183281. This user Mathcad (Luc Meekes) was the good old 11th version of the engine with a character from the Maple, and not from the MuPAD, which made it possible to solve the problem.