@WA573 I understand that.  What I am saying is that I have no idea how it corresponds to what is being computed in the worksheet. 

@WA573 Okay, I have no idea how your Fig corresponds to the expression in the worksheet.  Perhaps someone else can have a look and comment.

@WA573 Since you get the same answer through various approaches, maybe that's the right answer.  Why don't you like that answer?

Throughtout your worksheet you have things line conjugate(lambda1) and conjugate(lambda2), indicating that lambda1 and lambda2 are treated as complex numbers.  But then you have:

L := (limit(y4, t = infinity) assuming (lambda1 < lambda2));

How can lambda1 be less than lambda2 if these are complex numbers?

@C_R  As I noted earlier, I don't understand the OP's problem statement, perhaps because the statement is incomplete. The animation that I posted is something quite different. It consists of a rotating horizontal platter and a solid ball that rolls over it without slipping. The motion of the ball is completely determined by the equations of dynamics and the initial conditions. The dynamics imply that the center of the ball traces a circle, not a spiral.

I will be impressed if MapleSim can handle this. Post your solution if it succeeds.

Here are the parameters that went into producing my animation:

Radius of platter: R = 4
Radius of the ball: a = 1
Platter's angular velocity: Omega = 1
Ball's mass: m = 1
Ball's moment of inertia: J := 2/5*m*a^2

Initial condition (at t=0):
    Ball's center at (x,y,z) = (0.8, 0, 1)
    Ball's orientation: rotate about the x axis by 30 degrees
    Ball's angular velocity vector: omega = < 1/3, 1/5, 1/4 >  
    Velocity of the ball's center can be computed from the no-slip condition:
        x' =  a*omega[2] - y*Omega
        y' = -a*omega[1] + x*Omega
        z' = 0

@Earl If you expand the "...more" below the YouTube video, you will find a link there to an expository paper published in the American Journal of Physics where the equations of motion of the rolling ball are derived and solved.

That's not really an original research; the problem is an old classic and is included in many books on rigid body dynamics.

@Carl Love Some years ago I made an animation in Maple of a ball rolling on a platter and then made a movie out of it.  Here is it:

     ball-on-rotating-platter.mp4

I am not posting the worksheet since it calls on a couple of my own Maple libraries that will be useless to others.

@Earl I can't tell what problem is being solved in your worksheet.  As Carl has pointed out, "frictionless" makes no sense in this context.

Also regarding Carl's suggestion of analyzing the motion of a ball that rolls without slipping on a rotating platter, you may be interested in this video:

https://www.youtube.com/watch?v=3oM7hX3UUEU

That motion may be found exactly (no numerics) but the procedure is somewhat nontrivial.  It goes a bit beyond freshman physics.

@acer Thanks for confirming the issue and filing a bug report.

@Anthrazit That can be caused by a disk that is about to fail.

Maple is not equipped to handle numerical solutions of elliptic PDEs.  You may either write your own numerical solver -- that should not be very difficult if you know about finite differences -- or find another software that can do elliptic PDEs.

Short answer: They can be.

Long answer:  To get a more meaningful answer, you should post a more meaningful question.

@Suryakanth The PDEs involve a derivative of q2 but no boundary conditions on q2 are specified.

Suggestion:  Consider solving a few simpler problems to develop your understanding of how Maple works.  The problem that you are attempting to solve is much too difficult for a beginner.

The error message is very clear:

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same

That's because you are attempting to solve a system of six PDEs in seven unknowns.

@Gabriel Barcellos For publication-quality graphics, export the graphics as EPS (Encapsulated PostScript).  That produces vector graphics which may be included in a LaTeX document without a loss of quality.  If you need the graphics in the PDF format, apply an appropriate tool to convert the graphics from EPS to PDF.  Do not export directly from Maple to PDF as that embeds the graphics in a letter-sized (or A4) paper which is useless for further processing.   (This has been brought to Maplesoft's attention several times but the problem persists.)

Graphics posted on this web page are in the PNG format.  They are certainly not publication-quality graphics.

As to your question regarding the difference of quality between my version of the posted graphics versus yours, I don't see a detectable difference between the two graphics that you have posted other than the fonts of the tickmarks and labels.  As I noted in an earlier reply, that is done by specifying the font family and size, as in

plots[setoptions](font=[TIMES,12], labelfont=[TIMES,16]);
plots[setoptions3d](font=[TIMES,12], labelfont=[TIMES,24]);

You may include these in your Maple document—you actually need only the first one for 2D graphics—or you may put them in Maple's initialization file so that they apply to every graphics that you generate.