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f(w,t)=sin(wt)/w. Help make defined at w = 0. in c/math@lemmy.world
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f(w,t)=sin(wt)/w. Help make defined at w = 0. in c/math@lemmy.world
[–] [S] 4 points 2 months ago* (1 child)

I thought maybe with some clever algebra or calculus the function can be transformed into function that has outputs equal to current's:

limw->af(w,t)

Since the limit (AFAIK) is defined everywhere.

Also maybe(idk) dividing really small number by other really small number is numerically unstable? I use f32(32 bit float) on microcontroller.

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    • f(w,t)=sin(wt)/w. Help make defined at w = 0. in c/math@lemmy.world
    [–] [S] 3 points 2 months ago (3 children)

    Hello. I am a school student making an open source robot car.

    I did not ask my teammate, will do.

    Btw there is our repository: (Currently there is no proper README.md, docs). https://github.com/XLNC-APEX/WRO_FE_2026_NATIONAL

    You can see images and some steering, radius related experiment at my mastodon post. https://mas.to/@soupborsh/117011244080971088

    I prefer to not interact with AI, that is why I am writing here to humans.

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    • 8
    f(w,t)=sin(wt)/w. Help make defined at w = 0. (discuss.tchncs.de)
     

    Is there a way to make the function

    f(w,t)=sin(wt)/w

    defined at w = 0?

    I want to achieve better numerical stability, and make it continuous everywhere.

    Observation: Using limw->0 f(w,t)

    I know that at w = 0:

    f(0,t) = t

    Is it possible to improve this function? I would be really glad to know and why, how. Thank you in advance!

    I really do not want to code in smth like: if w < 0.001 { x = t; }

    Background notes: My equation also has constant v coefficient, but I removed it for simplicity. f(w,t)=v*sin(wt)/w

    If I derived this correctly this should be x component of a motion of a car that rotates with rate w. It goes with const speed and const steer.

    These are consts: v - speed, l - base length(dist from rear to front shaft), a - steering angle.

    w(a) is defined idk if correctly. w(a) = (vsin(2a))/(2*l) I just logically added proportions, projections, imagining a rear wheel powered car. Put some values I am somewhat confident in, such as: w(0) = 0 w(π/2) = 0