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#: ../../source/behavior/equations/equations.rst:2
msgid "Equations"
msgstr ""

#: ../../source/behavior/equations/equations.rst:4
msgid ""
"Although equations are probably the single most important mathematical "
"aspect of Modelica, they are also the simplest to explain."
msgstr ""

#: ../../source/behavior/equations/equations.rst:8
msgid "Basic Equations"
msgstr ""

#: ../../source/behavior/equations/equations.rst:10
msgid ""
"There are really no complicated semantics to explain about equations. All "
"equations are composed of a left hand expression and a right hand expression"
" separated by an equals sign, *i.e.,*"
msgstr ""

#: ../../source/behavior/equations/equations.rst:18
msgid ""
"Through the examples presented in this chapter, the reader has been exposed "
"to this pattern over and over again in each example.  The only real "
"deviation from the syntax shown above is the case where a description of the"
" equation is included as well, *e.g.,*"
msgstr ""

#: ../../source/behavior/equations/equations.rst:28
msgid ""
"As was pointed out previously, the left hand and right hand sides of an "
"equation in Modelica are expressions, not assignments.  In other words (and "
"in contrast to most programming languages), the left hand side does **not** "
"have to be a variable (as we can see in the case of Newton's law above)."
msgstr ""

#: ../../source/behavior/equations/equations.rst:35
msgid "Initial Equations"
msgstr ""

#: ../../source/behavior/equations/equations.rst:37
msgid ""
"As we saw in many of the examples in this chapter, it is possible to specify"
" equations within a model to be used to solve for initial conditions.  This "
"entire topic of initialization will be discussed in detail in the next "
"section, titled :ref:`initialization`.  For now, all we will say on this "
"topic is that if an equation is to be applied *only* to solve for initial "
"conditions, the ``equation`` section must be qualified by the ``initial`` "
"keyword as follows:"
msgstr ""

#: ../../source/behavior/equations/equations.rst:51
msgid "Conditional Equations"
msgstr ""

#: ../../source/behavior/equations/equations.rst:53
msgid ""
"In the next chapter, we'll discuss how to use ``if`` statements to represent"
" conditional behavior.  It is worth getting ahead of ourselves a little bit "
"to point out that equations can be conditional.  There are really two forms "
"of conditional equations. The first is the balanced form, *e.g.,*"
msgstr ""

#: ../../source/behavior/equations/equations.rst:67
msgid ""
"In the balanced case, the number of equations is always the same (1 in the "
"code above), but *which* equation can change.  This is important because to "
"simulate a model in Modelica, the number of variables must equal the number "
"of equations and the number of equations must be fixed during the "
"simulation."
msgstr ""

#: ../../source/behavior/equations/equations.rst:73
msgid ""
"The other type of conditional equations are ones where the number of "
"equations is unbalanced.  This means that the number of equations on the "
"``if`` side may not be equal to the number of equations on the ``else`` side"
" (like it was in the balanced case, previously)."
msgstr ""

#: ../../source/behavior/equations/equations.rst:80
msgid ""
"But remember, the number of equations cannot change during a simulation.  So"
" how is it then that the number of equations can be different from the "
"``if`` side to the ``else`` side?  It can only happen if **the value of the "
"conditional expression cannot change during the simulation**.  In order to "
"be able to ensure that the conditional expression can never change, it is "
"necessary that all variables in the conditional expression have so-called "
"*parametric variability*."
msgstr ""

#: ../../source/behavior/equations/equations.rst:89
msgid ""
"Remember in our discussion of :ref:`variability` the fact that variables "
"with the ``parameter`` qualifier cannot change during a simulation?  If a "
"variable with the ``parameter`` qualifier cannot change during a simulation "
"and all the variables in an expression have this parametric variability then"
" the entire expression must also have parametric variability (*i.e.,* the "
"value of the expression cannot change during a simulation)."
msgstr ""

#: ../../source/behavior/equations/equations.rst:97
msgid ""
"At this point, you might be asking yourself why this unbalanced case would "
"be useful?  Again, we are getting ahead of ourselves here, but one use case "
"would be the conditional application of initial equations, *e.g.,*"
msgstr ""

#: ../../source/behavior/equations/equations.rst:112
msgid ""
"In other words, if the Boolean parameter ``steady_state`` is true, then the "
"initial equations are enforced.  But if the parameter is false, they are "
"not.  The conditional expression here clearly has parametric variability "
"because the expression contains only a variable and that variable is a "
"parameter."
msgstr ""

#: ../../source/behavior/equations/equations.rst:118
msgid ""
"That's all we'll say on this topic for now, since discrete and conditional "
"behavior will be discussed in detail in the :ref:`next chapter <discrete-"
"behavior>`."
msgstr ""

#: ../../source/behavior/equations/equations.rst:78
msgid "parametric variability"
msgstr ""
