Rouben Rostamian

MaplePrimes Activity


These are replies submitted by Rouben Rostamian

@acer Setting adaptive=true gets around the problem. Thanks for your suggestion. 

I whittled down the original y to something as simple as y = 1 - cos(t) which exhibits the same issue:

y := 1 - cos(t);
plot(y^(3/2), t=0..2*Pi);

Your suggestion of adaptive=true gets around that problem but I find Maple 2023's default behavior is less than ideal.  I will file an SCR and hope that someone can look into this.

Why keep it a secret?  Tell us the function that you wish to plot!

@mary120 This is what your F looks like near phi=0:

You want to integrate 1/sqrt(-2*F). But F is positive just to the right of origin, so your integrand is complex there.

But I think that your problem lies elsewhere.  Note the vertical coordinates in that graph.  They are of the order 10^(-10).   How much do you trust the coefficients that enter the definition of your F?  Perhaps F(0)=0 and F<0 otherwise?  Does F actually have a root near phi=0.0013 as we see in the graph?  Extremely small changes in the coefficients can change the behavior of F and that can change the value of your integral drastically.

You need to examine the source of your F function and decide which part is meaningful and which is junk.  Try to plot F(phi) to see if it makes sense.

 

@yasi I can't tell what you are saying here.  Try to be more specific.

@JAMET The code you have posted is useless.  How is anyone going to test it?

To get helpful answers, you should learn how to upload your worksheet to this site.  Ask if you don't know how.

 

Do you know how to do that by hand?  If so, then the Maple implementation is quite trivial.

So to clarify, are you asking for the mathematical formulation or a Maple implementation?

@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.

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