Alexey Ivanov

## 1105 Reputation

10 years, 269 days

## I think he just changed his interests a ...

Looks like he's alive and well. Those who have lost hope of communicating with this person can find him, for example, here and here.

## For example, so...

allvalues(solve({eq1, eq2}, {A, B}));

## If I understand your problem correctly…...

For calculating the kinematics of the manipulator, Maple of almost any version is quite suitable directly. If a system of nonlinear equations is used to describe the model of a manipulator, then it is very easy mathematically to fix any desired degree of freedom.
Perhaps you can be useful the messages, which can be found at this link:
https://www.mapleprimes.com/posts/210003-Manipulator-With-Variable-Length-Of

## Event...

Is this way acceptable?
Lotka_Volterra_EVENT.mw

## For example...

restart;
f := d+(c*x^3+b*x^2)*(x-1)+(b*x^2+d)^3*(a+x);
expand(f);
sort(collect(expand(f), x), x, ascending);
sort(collect(expand(f), x), x, descending);

## plots[implicitplot3d]...

There is a universal approach in plots[implicitplot3d]. It can be used also for other equations.
(In the text, any combination of multiplication of two equations.)
composite_surfaces_MP.mw

## For example...

implicitplot(x^2*y^2-2*x*y^3+y^4-y^3+x^2 = 1, x = 100 .. 1000, y = 0 .. 1000, numpoints = 100000);

## fieldplot3d...

The first that came to mind

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])

## combine...

>? 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);

## >?dsolve[events]...

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]));

## The method of Draghilev...

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

## 15 - 3 = 12 ( variables)...

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.

## Drawing...

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.

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