Fix for broken equation

This commit is contained in:
Christian Risi 2025-02-16 12:22:01 +01:00
parent a6b3ab236e
commit a76ad76840

View File

@ -107,21 +107,24 @@ $$
>
> Then, put all variables equal to the previous one derivated:
>
> $x(t) = \begin{bmatrix}
> x_1(t)\\
> x_2(t) = \dot{x_1}(t)\\
> \dots\\
> x_n(t) = \dot{x}_{n-1}(t)
> \end{bmatrix}
> \;
> \dot{x}(t) = \begin{bmatrix}
> \dot{x_1}(t) = x_2(t)\\
> \dot{x_2}(t) = x_3(t)\\
> \dots\\
> \dot{x}_{n-1}(t) = \dot{x}_{n}(t)\\
> \dot{x}_{n}(t) = \text{our formula}
> \end{bmatrix}$
>
$$
x(t) = \begin{bmatrix}
x_1(t)\\
x_2(t) = \dot{x_1}(t)\\
\dots\\
x_n(t) = \dot{x}_{n-1}(t)
\end{bmatrix}
\;
\dot{x}(t) = \begin{bmatrix}
\dot{x_1}(t) = x_2(t)\\
\dot{x_2}(t) = x_3(t)\\
\dots\\
\dot{x}_{n-1}(t) = \dot{x}_{n}(t)\\
\dot{x}_{n}(t) = \text{our formula}
\end{bmatrix}
$$
Now in our state we may express `position` and `speed`, while in our
`next_state` we'll have `speed` and `acceleration`: