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Change last parts of dae.tex to sentence-based line breaks
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henrikt-ma committed Mar 16, 2022
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\chapter{Modelica DAE Representation}\label{modelica-dae-representation}

In this appendix, the mapping of a Modelica model into an appropriate
mathematical description form is discussed.
In this appendix, the mapping of a Modelica model into an appropriate mathematical description form is discussed.

In a first step, a Modelica translator transforms a hierarchical
Modelica simulation model into a ``flat'' set of Modelica
``statements'', consisting of the equation and algorithm sections of all
used components by:
In a first step, a Modelica translator transforms a hierarchical Modelica simulation model into a ``flat'' set of Modelica ``statements'', consisting of the equation and algorithm sections of all used components by:
\begin{itemize}
\item
Expanding all class definitions (flattening the inheritance tree) and
adding the equations and assignment statements of the expanded classes
for every instance of the model.
Expanding all class definitions (flattening the inheritance tree) and adding the equations and assignment statements of the expanded classes for every instance of the model.
\item
Replacing all \lstinline!connect!-equations by the corresponding equations of the connection set (see \cref{generation-of-connection-equations}).
\item
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Mapping all \lstinline!when!-clauses to equation sets (see \cref{when-equations}).
\end{itemize}

As a result of this transformation process, a set of equations is
obtained consisting of differential, algebraic and discrete equations of
the following form where ($v := \lbrack p; t; \dot{x}; x; y; z; m; \text{\lstinline!pre!}(z); \text{\lstinline!pre!}(m)\rbrack$):
As a result of this transformation process, a set of equations is obtained consisting of differential, algebraic and discrete equations of the following form where ($v := \lbrack p; t; \dot{x}; x; y; z; m; \text{\lstinline!pre!}(z); \text{\lstinline!pre!}(m)\rbrack$):
\begin{subequations}
\begin{equation}\label{eq:dae}
0 = f_{\mathrm{x}}(v, c)
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