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