@Carl Love I apologize Carl. The number 4 in the ODE should be 1. I have provide a link to a worksheet (correctly I hope) showing the physical situation from which the ODE is derived.

Rotating_Pendulum_explained.mw.

@Kitonum You have been a help to me on a number of occasions and I truly appreciate this. I hope you continue to provide cogent replies to my inquiries.

@Kitonum Does your solution assume the top is a hollow shell with all its mass in its surface?

If the top is solid with uniform density of one, is the following the correct calculation of its Moment of Inertia (MI) about the z axis?

int((1/2)*Pi*TopSC[1]^2*(TopSC[1]^2), z = 0 .. Pi)

The logic of the above integral is:

Integrate the MI of a cylinder (MI = (m*r^(2))/(2)),;
centred on the z axis (the top's axis of revolution), of height dz, radius = TopSC[1], ;mass = Pi*(TopSC[1])^(2)*dz, ;
from the top's bottom (z = 0) to its top (z = π).

 For anyone else answering, the top has a uniform density of one.

@acer Your suggestion works well and is more intuitive to me. I would like to praise your answer but I don't see a thumbs up or trophy icon in its header.

@Carl Love As usual, your answer is informative and to the point.

@Carl Love Hello Carl, I've examined all the ListTool commands but cannot find help text for operator ?[] which you used above. Is help available and if so how can I find it?

@Carl Love Thank you, Carl for the insight into the light ray vector and for several list manipulations in Maple that I was not aware were possible.

Sorry, plot3d parameter Plot3Daxes from my archive displays boxed, colored axes.

@Kitonum I have gratefully learned several coding techniques from your examples. Thank you.

On examining an open umbrella, it appears that the surface between a pair of ribs in not a portion of a sphere but a minimal surface.

Is this true? Does any Maple resource (Maple Primes, Maple Application Centre, Maple package) demonstrate or provide the code for calculating and displaying such a surface?

@Markiyan Hirnyk Thanks for pointing me to the appropriate help page, I don't know how I overlooked it.

@Jarekkk I hope you receive this question to an old answer.

The solve commands in your answer above work in Maple 2016.0 but I can't find an explanation of the 'parametric' or 'parameters' options in Maple 2016.0 help.

Where can I find help text explaining these options?

@dharr Both DirectSearch.mla and DirectSearch.hdb were in the path displayed by command currentdir() when I issued the HelpTools migrate command. The .hdb file size is 2711 MB but the migrate command produced a DirectSearch.help file whose size is 56 MB. This small size led me to say that the .help file had no content.

@tomleslie Thanks, but I don't have Maple 2015 having just upgraded from Maple 15 to Maple2016. Is there any other way?

@Kitonum Greeting. It seems the overflow error occurs only in Maple 15.

When the following statement in procedure Picture above...

P[i]:=seq([subs(var=var1+i*h,e1), subs(var=var1+i*h,e2),0], i=0..N) fi; fi; od;  #`  MODIFIED FOR 3 D `[f(t), g(t), 0] 

...  is replaced by ...

if nops(L[i, 1]) = 2 then P[i] := seq(subs(var = h*i+var1, [e1, e2]), i = 0 .. N) else

e3 := L[i, 1, 3];

P[i] := seq(subs(var = h*i+var1, [e1, e2, e3]), i = 0 .. N) end if:

... then the following list displays a pretty seashell shape

L := [[[0, 0, 0]], [[cos(a), sin(a), (1/3)*cos(8*a)], a = 0 .. 2*Pi]]