Alexey Ivanov

## 17 Badges

12 years, 100 days

## Because there are strict zeros...

Since childhood, I try to avoid strict zeros in coordinates (and generally avoid strictly identical values) due to formulas, because expressions may be nullified after substitution. It is better to shift the point o or d along the oX axis, for example:

```restart:
with(geometry):
point(o, 0.1e-11, 0.);
point(A, 0., 1.);
point(d, 0., 2.);
point(F, .8944271920, 1.4472135960);
line(lOD, [o, d]);
line(lAF, [A, F]);
alpha := FindAngle(lOD, lAF);
```

alpha = 1.107148718

## For example...

CompleteSquare(x^2+y^2-2*x-y-2 = 10, x);

## Try solve...

```restart:
EQ1:=-1958143.922*k*wr+2468.8339*k^3*wr-0.9481118254e16*k^2-114000.8376*k^4:
EQ2 :=-1186578.220*R*k^2*wr-312683.0293*k^5-288960.9621*k^3*R:
allvalues(solve([EQ1, EQ2], [k, wr]));```

## 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")

## And what about nops?...

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

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

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