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f(w,t)=sin(wt)/w. Help make defined at w = 0. (discuss.tchncs.de)
submitted 2 months ago* by to c/math@lemmy.world
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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

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[–] 5 points 2 months ago (1 child)

If you want to do it yourself instead of using a math library, then my immediate thought is tp write out and calculate the Taylor series of your function. sin(x) is basically x +x^3 + x^5 +... with appropriate constants (look them up on wikipedia) so then sin(x)/x is the same thing but you divide all the parts by x so you're gonna have c + x^2 + x^4 + ... Now just add more parts in a while loop until the error term is small enough or you have spent some maximal number of allowed iterations and you're good.

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