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These are replies submitted by Kitonum

@tomleslie  Thanks. I didn't know that Maple accepts systems written in vector form. The help (Maple 2018) does not say about this.

@jalal  Nice! Only the shape of the heart needs to be slightly stretched horizontally.


Anim4 := animate(textplot, [[op(convert(Position(t)+(1.3/4)*Vitesse(t), list)), `#mover(mi("V"),mo("→"))`], align = [right, below], font = [times, bold, 18]], t = t0 .. t1, frames = 100):


@acer  I thought this trait was just a typo, since in further transformations OP assumes that all symbols are real and positive.


1. Look closely at the picture. The coordinates of several points in your solution do not match what we see. If we assume that point  A  is on the coordinate plane  yOz, then there should be  A(0,6,2), B(-3,0,4), C(5*cos(Pi/3),0,5*sin(Pi/3))

2. Of course, if the coordinates of all points are known, then there is no problem in finding any angles. This can be done using geom3d package or in any other way. The problem is that the condition also contains 2 forces and this obviously should be taken into account in the solution.

3. To include these forces in the solution, I assumed that the OA rod is not rigidly fixed in the wall, but simply rests against it and at the same time can freely tilt to any side. I also assumed that the first coordinate of point A is unknown (it is not entirely clear from the figure whether point  A lies in the plane  yOz  or is shifted to the side). Under these assumptions, we have 3 unknowns and 3 equations for finding them, relying on static equilibrium (see my solution for details).


@yangtheary All answers in the last lines of code. I have added the required notation for clarity.

@Yo  You must provide a list of the main variables:

degree(alpha*x[1]^3+beta*x[1]*x[2]^2, [x[1],x[2]]);


In Maple 2018.2 on Windows 10, there is no such problem. All settings are the same as yours:

@lcz  See my upgraded answer.



eq := cos(2*x)-sin(x)*(sin(x)^2+1)^(1/2)+cos(x)^2*sin(x)/(sin(x)^2+1)^(1/2):
subs([cos(2*x)=1-2*sin(x)^2, cos(x)^2=1-sin(x)^2], eq);


Or more automatically

eq := cos(2*x)-sin(x)*(sin(x)^2+1)^(1/2)+cos(x)^2*sin(x)/(sin(x)^2+1)^(1/2):
expand(subs(x=arcsin(y), eq));
subs(y=sin(x), %);


@OscarSteenstrup  These are simply parametric equations of a conical surface, where polar coordinates on the yOz plane are taken as parameters.
If the equation of a curve on a plane  xOy  in Cartesian coordinates is  f(x,y)=0  and this curve rotates around the  Ox-axis, then the equation of a surface of revolution is  f(x, sqrt(y^2+z^2))=0 . Your cone can also be defined by this equation. The point is that if the surface is specified parametrically, then the quality of the drawing is usually much higher. See

plots:-implicitplot3d(eval(f, y=sqrt(y^2+z^2)), x=0..12, y=-5..5, z=-5..5);


@Scot Gould  You missed  the theta variable before the tangent.

@Johan159  Should be

plot(x->f(x,5), 0..10, labels=[x,z]); # The curve in 2D
plot3d(f, 0..10, 5..5, axes=normal, labels=[x,y,z]); # The same curve in 3D


@Preben Alsholm  Thank you.  In general case, you are right, but in this example there is no error, because

series(cos(x),x=0, 6) = series(cos(x),x=0, 5);

@Qruze  This is strange. I do not have Maple 2020 and cannot test this behavior. But this code in Maple versions 2015 - 2018 solves the example without any problems.


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