Constant speed
04-13-2016, 03:29 PM (This post was last modified: 04-13-2016 03:30 PM by Martin Hepperle.)
Post: #11
 Martin Hepperle Senior Member Posts: 333 Joined: May 2014
RE: Constant speed
(04-11-2016 03:53 PM)Tugdual Wrote:  ...
Thanks Martin, sounds like a good answer but I struggle with further conclusions.
First, at constant speed, I would assume that ds/dt = 0 so dx = 0?
Other question is how do you move from your expressions to a parametric equation for x(t) and y(t) over the time?

Almost ... constant speed would be $$v = {ds \over dt} = const.$$ not zero.
where: $$ds$$ ... distance and, $$dt$$ ... time interval.

Using a given (constant) speed $$v$$ and a (user selected) time step $$dt$$ you would determine $$ds = v \cdot dt$$ and then use the equation above to find $$dx$$.
You would start at e.g. time $$t=0$$ at position $$x=0$$, calculate $$dx$$ for the given speed, march to $$x=x+dx$$ and plot $$f(x)$$ at the new point (for time $$t=t+dt$$. Then repeat for the next time step.

My simple equations will work as long as the function is monotonic $$y=f(x)$$. For a parametric curve (e.g. a circle) one would have to rewrite with the parameter $$t$$ or $$s$$ (arc length) to obtain $$dx$$ as well as $$dy$$ as a result.
This is left as an exercise to the inclined reader ... ;-)

Martin
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 Messages In This Thread Constant speed - Tugdual - 04-04-2016, 10:33 PM RE: Constant speed - PANAMATIK - 04-05-2016, 07:01 AM RE: Constant speed - Tugdual - 04-05-2016, 07:19 AM RE: Constant speed - Dave Britten - 04-05-2016, 11:14 AM RE: Constant speed - Tugdual - 04-05-2016, 06:04 PM RE: Constant speed - Dave Britten - 04-06-2016, 11:16 AM RE: Constant speed - Tugdual - 04-07-2016, 06:13 AM RE: Constant speed - Dave Britten - 04-07-2016, 11:16 AM RE: Constant speed - Martin Hepperle - 04-11-2016, 02:01 PM RE: Constant speed - Tugdual - 04-11-2016, 03:53 PM RE: Constant speed - Martin Hepperle - 04-13-2016 03:29 PM RE: Constant speed - Tugdual - 04-13-2016, 06:30 PM RE: Constant speed - Martin Hepperle - 04-18-2016, 07:27 AM

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