f(w,t)=sin(wt)/w. Help make defined at w = 0. by soupborsh in c/math@lemmy.world
[-] soupborsh@discuss.tchncs.de 2 points 4 days ago

Taylor series are really cool, thank you! I would choose up to 3rd power of x and up until x is less that pi/6 it is good enough for me. sinc and (1-cos(x))/x some Taylor polynomials plots typst code

Everyone's asking, 'Who's Json?', but nobody's asking, 'How's Json?' by soupborsh in c/programmer_humor@programming.dev
f(w,t)=sin(wt)/w. Help make defined at w = 0. by soupborsh in c/math@lemmy.world
[-] soupborsh@discuss.tchncs.de 4 points 2 weeks ago* (last edited 2 weeks ago)

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

lim~w->a~f(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.

f(w,t)=sin(wt)/w. Help make defined at w = 0. by soupborsh in c/math@lemmy.world
[-] soupborsh@discuss.tchncs.de 3 points 2 weeks ago

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.

8
f(w,t)=sin(wt)/w. Help make defined at w = 0. (discuss.tchncs.de)
submitted 2 weeks ago* (last edited 2 weeks ago) by soupborsh@discuss.tchncs.de to c/math@lemmy.world
14 comments fedilink

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 lim~w->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

soupborsh

joined 3 weeks ago