[Tex/LaTex] equation number to caption

Question

I am trying to change the number in the caption of the figure. It should be the following number of the equation. So instead of "Gleichung 0.1" i want "Gleichung 0.2" in the caption (see picture). I don't mind typing those numbers manually, since it's only for 4 following figures that have to follow on the equation number. Plus i don't have any other equations afterwards, in that chapter (if it helps). But i have a lot of figures following, which numbers should not be changed! I have tried a couple of instructions i've found like:
\usepackage{chngcntr} or something similar, but i couldn't figure it out yet.
That's why i come to you with this MWE.

If i could keep the figure command and type in the numbering manually without changing the numbers of the following figures, you would help me already;)

EDIT: The actual document and numbering is shown in the last picture.

MWE:

\documentclass{scrreprt}
\usepackage{amsmath, amssymb}

\begin{document}

\begin{equation} 
\label{eq:periodischefunktion}
f(t)=f(t+T),
\end{equation}

\begin{figure}[ht]
\renewcommand*\figurename{Gleichung}
\[
\left|
\begin{array}{*{3}{c}}
c_{F_x\vec{x}} & c_{F_y\vec{x}} & c_{F_z\vec{x}}\\
c_{F_x\vec{y}} & c_{F_y\vec{y}} & c_{F_z\vec{y}}\\
c_{F_x\vec{z}} & c_{F_y\vec{z}} & c_{F_z\vec{z}}\\
\end{array}\right|_{stat} = 
\left|
\begin{array}{*{3}{c}}
410,6 & - & -\\
- & 318,7 & -\\
- & - & -\\
\end{array}
\right|
\frac{\mbox{N}}{\mbox{mm}}
\]
\caption{Steifigkeitsmatrix bei Auskragung $A=0$~mm}
\label{eq:steifmatrix0}
\end{figure}

\end{document}

Answer 1

This can go wrong if the figure floats after LaTeX has typeset other numbered equations, but here it is anyway:

\documentclass{scrreprt}
\usepackage{amsmath, amssymb,siunitx}

\begin{document}

\begin{equation} 
\label{eq:periodischefunktion}
f(t)=f(t+T),
\end{equation}

\begin{figure}[ht]
\renewcommand*\figurename{Gleichung}
\makeatletter
\let\c@figure\c@equation
\makeatother
\[
\begin{vmatrix}
c_{F_x\vec{x}} & c_{F_y\vec{x}} & c_{F_z\vec{x}}\\
c_{F_x\vec{y}} & c_{F_y\vec{y}} & c_{F_z\vec{y}}\\
c_{F_x\vec{z}} & c_{F_y\vec{z}} & c_{F_z\vec{z}}\\
\end{vmatrix}_{\mathrm{stat}} = 
\begin{vmatrix}
410,6 & - & -\\
- & 318,7 & -\\
- & - & -\\
\end{vmatrix}
\si[per-mode=fraction]{\newton\per\milli\meter}
\]
\caption{Steifigkeitsmatrix bei Auskragung $A=\SI{0}{\milli\meter}$}
\label{eq:steifmatrix0}
\end{figure}

\begin{figure}[ht]
Normal
\caption{Normal figure}
\end{figure}

Some reference to \ref{eq:steifmatrix0}.

\end{document}

The trick is to make (locally) the caption in the figure environment use equation.