[mmaimcal]Re: [Almasci] Antenna Acceleration

[Richard Hills]

Dear Mark,

OK.  Here (page 2 of the spreed sheet) is your position function and then an
interpolation using cubics for each interval in the same way as I did before. 
(I am assuming that you can at least open the spreadsheet somehow and see the
picture?)  The lines are right on top of each other as you would expect.  I
have plotted the difference as well - multiplied by 1000 - and you can see it
is small.  This would be much less than a second of arc and since this is just
at the turnaround I think this is fine.

I am somewhat puzzled by the form of the error since I think the match to both
the position and velocity should be perfect at each 0.048 sec interval and it
looks as if the postion is right but the velocity is not - i.e. the slope of
the error isn't zero at these points.  I don't have time to investigate more
tonight.

If you do want to play with it I have written out the expression for the
interpolation at the top of the file.  Here x0 and v0 are the position and
velocity at the start of each interval and x1 and y1 are the values at the end
of it.  I personally think we have done this to death now so I don't think
more work is needed on the details.  More helpful would be confirmation from
someone on the control side that we are making the right assumptions about how
the system is expected to work.

Best Richard
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