An easy setup for the uni's Draghilev method for plot implicit plane curves.
Best regards.
Alvaro.

dm_revisited_correct.sm (34 KiB) downloaded 220 time(s).

Original Uni's Dragilev works fine 6179, not your latest SS 6179.
Keep up Alvaro !

Hi Jean.

This version works in the SMath cloud:

https://en.smath.info/cloud/worksheet/E77mF78o ,

android, and in the last portable version (0.99.6839).


dm_revisited.sm (34 KiB) downloaded 116 time(s).

Best regards.
Alvaro.

Guys, please write correctly: Draghilev.

Thank you, Alvaro, very nice.

dm_revisited1.sm (23 KiB) downloaded 134 time(s).

Wrote

Thank you, Alvaro, very nice.

dm_revisited1.sm (23 KiB) downloaded 134 time(s).

Thanks you, Ber. Just an apologize, I upload the first time the wrong file, where I use for(3), the correct is this one, with for(4) arguments version (with for(3) seems that you can't change the iterating variable in the body of the loop, but for(4) do that).

This have not effect in the function DM.2(f(2),uo,ho,N), which use RK2 method, but solve an issue in DM.2(f(2),uo,ho,N,K)

dm_revisited_correct.sm (34 KiB) downloaded 124 time(s).

With the last argument different from 0 you call a RK5, which colud be faster for some figures:



Best regards.
Alvaro.

Draghilev’s method.
For example, inverse kinematics problem of manipulators. (This applies both to platforms and to manipulators with any number of links and any number of degrees of freedom.)
Implemented in the Maple environment. More detailed information can be obtained from the links. The last reference to the universal method of kinematic analysis of spatial and planar link mechanisms with any number of degrees of freedom. Published in the applications center of MapleSoft.

https://www.mapleprimes.com/posts/208958-Determination-Of-The-Angles-Of-The-Manipulator

https://www.mapleprimes.com/posts/209255-The-Use-Of-Manipulators-As-Multiaxis

https://www.mapleprimes.com/posts/202821-Calculating-Linkage-Mechanisms#comment202349

Wrote

Guys, please write correctly: Draghilev.

Thanks! It's very important use the correct reference. But actually I'm not sure about the correct name: Google traductor isn't an authority for me, and I prefer to trust in your knowledge, but:

Translating to spanish it is: https://translate.google.com.mx/#ru/es/%D0%B4%D1%80%D0%B0%D0%B3%D0%B8%D0%BB%D0%B5%D0%B2



To english, from http://forum.exponenta.ru/f-x-0-t3892.html



From google academic: https://scholar.google.com/scholar?hl=es&as_sdt=0%2C5&q=author%3A%22a+v+dragilev%22&btnG=



Form http://www.mathnet.ru/php/person.phtml?&personid=32359&option_lang=eng



and ( http://www.mathnet.ru/links/3c8499a4720a6eb7bcfc74a0694d5b23/de9397.pdf )



and some others.

Maybe someone can contact the author or some friend of him.

Best regards.
Alvaro.

Please do not give dubious arguments. It was the request of Anatoly Vladimirovich Draghilev himself. Writing in a different version occurred besides his desire.
Драгилев Анатолий Владимирович (1923-1997).
If this means nothing to you, then, of course, you are entitled to do what you want.

Wrote

It was the request of Anatoly Vladimirovich Draghilev himself.

Good to know

Wrote

If this means nothing to you, then, of course, you are entitled to do what you want.

I don't think "it means nothing to him", but it worth to mention that you might found many results on search engines if you search Dragilev as well as Draghilev (typos in internet spreads like flu, knowledge is the cure; unfortunately there isn't a very large documentation about him in english, that doesn't help).

It was a big problem to bring the idea of Anatoly Vladimirovich for the Russian-speaking audience. To do this in English turned out to be quite a simple matter. But here, as we see, there is a misunderstanding with the spelling of a name in another language.
I think the main thing is that we know who we are talking about.

Hi. I post this example of the uni's procedure implementation because not just it's more easy for some curves, but it show that we don't need to use the parameter, even the original procedure talks about the parametrization of the curve (one of them, the other, as uni explain in other forums, and apply he and others here, is for search intersection of curves).

Both Runge Kutta algorithms RK2 and RK5 in the numerical procedure don't achieve the "time", this is, the parameter, and the function D(t,x) usual in the rk solvers is just D(x) formed only by elements of the jacobian. This situation seems to me that even the algorithms came from derivatives, looks more like a global property of the function more than a local one, like the case of the derivative (local) and it inverse, integration (global).

During my (very) little researching I found Draghilev writing without h, and take it as the good one, but don't pay much attention about it. In spanish, we never use an h in this place; if we want to change the pronunciation of the "g" we can write "gi", "gui" or "güi", but not "ghi". Actually I have not idea about the difference in the pronunciation of Draghilev with or without the h.

As I say before, I respect the observation from Alexei and change the name in the last SMath file after his appointment.

Another thing that I make a mistake was to think that Draghilev was alive, I don't found any reference about his year of death.

Best regards.
Alvaro.

The classical Draghilev’s method. Example of solving the system of two transcendental equations. For a single the initial approximation are searched 9 approximate solutions of the system.
(4*(x1^2+x2-11))*x1+2*x1+2*x2^2-14+cos(x1)=0;
2*x1^2+2*x2-22+(4*(x1+x2^2-7))*x2-sin(x2)=0;
x01 := -1.; x02 := 1.;
https://vk.com/doc242471809_392966449
Example text on Maple here
https://www.mapleprimes.com/posts/200585-Draghilevs-Method-Fx0-Animation

it is description of the part of idea in English
https://www.maplesoft.com/applications/view.aspx?SID=149514

Full description in Russian
https://vk.com/doc242471809_437831729

Wrote

Please do not give dubious arguments.
It was the request of Anatoly Vladimirovich Draghilev himself.
Writing in a different version occurred besides his desire.
Драгилев Анатолий Владимирович (1923-1997)

The attached human eye by Draghilev method is From Uni [from recollection].
Supplementary tutoring for myself.
If you find some volunteers to code Tom G. Mathcad contour ... please feel free.
By the way, I have seen Uni in the PTC forum, specifically about Draghilev

Cheers ... Jean

Contour_9 Draghilev [Human eye].sm (31 KiB) downloaded 109 time(s).
Contour SOLVE Tom MCD.sm (198 KiB) downloaded 114 time(s).

Wrote

The classical Draghilev’s method. Example of solving the system of two transcendental equations. For a single the initial approximation are searched 9 approximate solutions of the system.
(4*(x1^2+x2-11))*x1+2*x1+2*x2^2-14+cos(x1)=0;
2*x1^2+2*x2-22+(4*(x1+x2^2-7))*x2-sin(x2)=0;
x01 := -1.; x02 := 1.;
https://vk.com/doc242471809_392966449
Example text on Maple here
https://www.mapleprimes.com/posts/200585-Draghilevs-Method-Fx0-Animation

it is description of the part of idea in English
https://www.maplesoft.com/applications/view.aspx?SID=149514

Full description in Russian
https://vk.com/doc242471809_437831729

Hi.

I don't see there a full explanation about the Draghilev method. I see only an application for the method, the seek for roots of a system of equations. That could give a poor idea about the meaning, importance and interpretation of the method.

The method it's about the parametrization of a function f:R^n -> R.



For instance think at anything more easy to do with the parametric equations rather than cartesians, and you get a new application for the Draghilev method.



In this file, maple is used only as symbolic solver for the ode's.
dm.sm (84 KiB) downloaded 120 time(s).

Best regards.
Alvaro.

Wrote

I don't see there a full explanation about the Draghilev method. I see only an application for the method, the seek for roots of a system of equations. That could give a poor idea about the meaning, importance and interpretation of the method...

Do you have poor eyesight or do not want to use a google-translator?

Full description in Russian
https://vk.com/doc242471809_437831729

Wrote

Do you have poor eyesight or do not want to use a google-translator?

Alexei, If I had vision problems, do you really think that could affect my understanding of a problem?

Here is an example of what can be called a fairly complete description of a particular issue:

https://en.wikipedia.org/wiki/Lagrange_multiplier

There you can see a very simular introduction of a formal parameter for minimize a nonlinear system of equations.

I insist: the power and originality of the Draghilev method isn't in solve a nonlinear system by a numerical method in the same way that we can minimize a nonlinear system by the Lagrange multipliers, but in obtain a parametrization for that system. Once you get it, there are a lot of more applications, like the surface area or the length for the curve defined for the original equation, by numerical or symbolic methods as you can see, if you want, in my previous post.

Best regards.
Alvaro.

Wrote

I don't see there a full explanation about the Draghilev method.

It plots contours: Electron function, Human eye bot lobes
but fails that one ! Maybe Dragilev is not so perfect.

BTW, Alvaro: Your last document like most if not all
create "Syntax error" the coding is freaked of all sorts of symbols.
I have that only with your work sheets ... but don't worry.

Jean

Page0 DraghilevRemToDo.sm (42 KiB) downloaded 100 time(s).

Wrote

Wrote

I don't see there a full explanation about the Draghilev method.

BTW, Alvaro: Your last document like most if not all
create "Syntax error" the coding is freaked of all sorts of symbols.
I have that only with your work sheets ... but don't worry.

Jean

Page0 DraghilevRemToDo.sm (42 KiB) downloaded 100 time(s).

Hi Jean. Try this, in the last portable version (0.99.6839.38235):
dm_portable.sm (81 KiB) downloaded 119 time(s).

If can't see it, try this other in the cloud:
https://en.smath.info/cloud/worksheet/zDTMw5p2

Best regards.
Alvaro.

Razonar, you are not talking about the method of Draghilev, but about your understanding of it. This is not the same thing. And: what is the relation to the essence have the lengths of the arcs, parametrization...? The main thing in the Draghilev method is the solution of a homogeneous system of linear equations by the Cramer method, when a certain value is given to a free variable in order to avoid division by 0. Everything else relates to the methods of implementation and to the areas of application.

Please be examined carefully, and then, perhaps, your contribution to a future article in Wikipedia about the Draghilev method will be the best in the world.