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These are replies submitted by Earl

@Christopher2222 Thanks for these references. I have some experience with a clothoid as a vertical element of a roller coaster so I will explore that as a transition curve.

Below is a worksheet containing a crude attempt to display a banked track end joined to a straightaway whose banking increases to the end track's banking as it extends towards the latter. However the straightaway does not approach the banked end on a straight line ( the y axis) as it should.

Is there a way to define the TransitionTrack to correct this?



@Carl Love I read Wikipedia's description of logarithmic differentiation and learned a lot. Much appreciated.

@Kitonum Thank you again.

@Kitonum Another good lesson from you!

I did not know that a double quote preceding an indeterminate causes it to be treated as a symbol only, i.e. not evaluated.

Is this feature mentioned anywhere in Maple help?

@Mariusz Iwaniuk Thank you. It seems Maple's DiffTutor invokes Maple's ShowSolution command. This will come in handy for future explanations.

@Kitonum Thank you for informing me of Maple's ShowSolution command. It will come in handy for future explanations.

@Carl Love I find your hint of taking the log of both sides of y(x) to be a simpler (clearer) route to the final derivative than the steps given by Maple's Student aids.  

@Joe Riel Thanks for this advice.

@Carl Love Thanks to you (and the quite dense Maple help) I now have at least a rudimentary understanding of the meaning of specfunc and I now understand the output of my statements E, F and G.

And thank you for the hint of using applyop in place of subsop and for your kind offer of further help with any future question I may have in using specfunc.


@Carl Love Thank you. New Maple info always helps.

@vv Thank you once again for adding to both my Maple and math knowledge. 

BTW, the construction U^+ gives an " invalid power" error message in my Maple 2016. I changed this to Transpose(U).

@Carl Love I hope the uploaded worksheet is the kind of example you desire. If not I can copy and paste the code in a reply.


@Carl Love I have reposted OnionExtended without the reference to my personal library and fully executed with plots inline rather than in windows. I hope you can access it. I'll also do this in future uploaded worksheets.


@Kitonum Your excellent replies and posts often inspire me to interesting modifications


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