|
|
|
Can easily show convergence:
$$ e^n\rightarrow 0 \hbox{ as }\Delta t\rightarrow 0,$$
because
$$
\lim_{\Delta t\rightarrow 0}
\tilde\omega = \lim_{\Delta t\rightarrow 0}
\frac{2}{\Delta t}\sin^{-1}\left(\frac{\omega\Delta t}{2}\right)
= \omega,
$$
by L'Hopital's rule or simply asking sympy:
or WolframAlpha:
>>> import sympy as sp
>>> dt, w = sp.symbols('x w')
>>> sp.limit((2/dt)*sp.asin(w*dt/2), dt, 0, dir='+')
w
|
|
|