one man

Alexey Ivanov

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8 years, 258 days
Russian Federation

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restart: with(plots): with(plottools):
c := fieldplot3d([r*sin(t)*cos(p), r*sin(t)*sin(p), r*cos(t)], r = 1 .. 2, t = 0 .. 2*Pi, p = 0 .. 2*Pi, coords = spherical, grid = [25, 25, 25]):
s := sphere([0, 0, 0], 1, color = white, style = surface):

display(c, view = [-1 .. 1, -1 .. 1, -1 .. 1]);
display(c, s, view = [-1 .. 1, -1 .. 1, -1 .. 1])

>? trig
combine(A*B,trig);

For example:
simplify(sin(x)*cos(y)+cos(x)*sin(y),trig);
and
combine(sin(x)*cos(y)+cos(x)*sin(y),trig);
 

It seems very simple:


eps=0.001;
lp:=dsolve(....,type = numeric, events = [[x(t) = 0-eps, [halt]]], range = ta .. te);

(and search the forum, for example: "halt")

For example, nops(solve(x^2+x+1,[x]));

nops(solve([f1(x1,...,xn),..., fn(x1,...,xn)],[x1,...,xn]));

To find the roots of the system of equations NxN, the method works as follows. The initial values of the system of equations NxN we define ourselves. An additional variable with initial value 1 is introduced,  as in the homotopy method, and after that, solving a known system of differential equations, we follow the change of sign of this additional variable. The place where the new variable changes sign be the solution of the original system of equations NxN. 
sistema9_1.mw
As we see, several solutions were found for one initial approximation.

As for the normalization of variables in the differential equation, there is no need for this way of applying  the Diaghilev  method.

And another example with two equations
https://www.mapleprimes.com/posts/200585-Draghilevs-Method-Fx0-Animation

If we look at your first message, it turns out that
r22 = r33, r23 = -r32, and they depend on x, then your system of equations has 15 - 3 = 12 variables.
 And the system of equations is not polynomial.

On the worksheet paste the picture from the buffer (ctr + v), click on the picture, and the "Drawing" panel starts to work. Learn the tools of the panel and work.

Topic on the Russian-speaking forum
http://dxdy.ru/topic94428.html 

   Here is an example of the movement of a point along the graph together with the output values of function and the coordinates. 
If you look at this place from the text, then maybe it will help?
http://www.mapleprimes.com/questions/205606-Find-Root-Method#answer219932  

a := [cos(x) = 0, 1, sin(y)*cos(x)-0.5 = 0];
a := convert(a, Vector); a(1); a(3);
whattype(a);

 convert(a,Vector[column]) or  convert(a,Vector[row])

> restart:
a := .9;
plots[display](plottools[cuboid]([-a, -a, -a], [a, a, a], transparency = .8, color = pink), plottools[sphere]([0, 0, 0], 1., style = surface, color = khaki), axes = none, view = [-a .. a, -a .. a, -a .. a]);

For example, you may draw using the "drawing" in any desired place of the graph (Although it is unlikely to fit you)

"

    The theory, if anything, here:
http://www.mapleprimes.com/posts/204684-Lever-Mechanisms-

    You can select and change any values, and then watch the result. Only the first you will be examined with the text. The text is small.  
 FOR_MP_2.mw   Maple15
    Hello your teacher! 

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