RetroFedf(w,t)=sin(wt)/w. Help make defined at w = 0.
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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People are being kind of rude, sorry about that.
I also think they aren’t understanding your problem. You have a function f(w,t) = sin(wt)/w which is well defined everywhere (in the sense of limits at w=0 ), but for which the naive implementation (compute sin(wt), then divide by w) gives the “wrong” output for w=0 (an error instead of t).
Note that the function sin(x)/x has a name, sinc(x). Using this to rewrite your function gives f(w,t) = sin(wt)/w = tsin(wt)/(wt) = tsinc(wt).
Now you just need to find a quality implementation of sinc from a math library.
Yes, when w->o, sin(wt)/w -> 1
(and hopefully sinc(0)=1 in any math library),
but also when t->0, sin(wt)/w -> 0.
I know that 0x1=0, but it’s not true that there’s a continuous function from the plane to the reals based on sin(wt)/w and OP has an interesting problem trying to decide what to do there.
Your answer gives much more accurate answers near zero and is absolutely the best practical solution, but the question of actual zero is interesting and might need context to decide what’s best.
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.
You’re right that limw->0 sin(wt)/w = t, because for small values of x, sin(x) is increasingly close to x,
but unfortunately limt->0 sin(wt)/w=0 because sin(0)=0
@Buildout has a good solution for the computation problem - a math library with sinc will compute t sinc(wt) much better than trying to compute sin(wt)/w for small values of w.
I don’t know what’s going on in the real world context when w or t are zero - this is an interesting question. Are either or both of them likely to actually be zero (or close enough that your processor uses zero to represent the number)? If so, can we deduce whether f(0,0)=1 or f(0,0)=0 is a better answer? Maybe f(0,0)=0 gives more surprising and jerky behaviour than f(0,0)=1, but I can’t be certain of that.
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So… you want to define division by zero?
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.
Ahh yeah, I misunderstood what you were going for, sorry! Yeah, check out Buildout’s suggestion!
this seems like a standard problem. did you discuss it with your colleagues? alternatively, did you already ask chatgpt? where are you struggling?
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.
yeah and i prefer not to interact with people who seek help who apparently didn’t put any work into trying to solve the problem themselves first
Then don’t comment.
If you don’t like answering questions, then simply don’t, and if you just like shitting on students asking questions then please just shut the fuck up and grow up.
We all start somewhere and asking people for help is absolutely NOT the massive moral and studying failure you’re making it out to be.
If you’d put anywhere near as much thought and effort into the mathematics as you did into gatekeeping learning, you’d see that there’s a genuine issue approaching zero from different directions in this function RxR->R and it’s not obvious what to do about that.
This is not stackoverflow. Stackoverflow was dying before LLMs, and it’s this kind of critical and/or hostilenon-answering response to beginners’ questions that killed it.
You can’t be bothered to think about or answer the question, and somehow you’ve concluded that the student who has actually done some work on the project is the lazy one who needs to be belittled.