# 
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#: ../../source/behavior/equations/first_order.rst:4
msgid "Simple First Order System"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:6
msgid "Let us consider an extremely simple differential equation:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:10
msgid ""
"Looking at this equation, we see there is only one variable, :math:`x`.  "
"This equation can be represented in Modelica as follows:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:23
msgid ""
"This code starts with the keyword ``model`` which is used to indicate the "
"start of the model definition.  The ``model`` keyword is followed by the "
"model name, ``FirstOrder``.  This, in turn, is followed by a declaration of "
"all the variables we are interested in."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:28
msgid ""
"Since the variable :math:`x` in our equation is clearly meant to be a "
"continuous real valued variable, its declaration in Modelica takes the form "
"``Real x;``.  The ``Real`` type is just one of the types we can use (a more "
"complete description of the various possibilities will be discussed in the "
"upcoming section on :ref:`variables`)."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:34
msgid ""
"Once all the variables have been declared, we can begin including the "
"equations that describe the behavior of our model.  In this case, we can use"
" the ``der`` operator to represent the time derivative of ``x``.  Thus,"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:43
msgid "is equivalent to:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:47
msgid ""
"Unlike most programming languages, we don't approach code like this as a "
"\"program\" that can be interpreted as a set of instructions to be executed "
"one after the other.  Instead, we use a Modelica compiler to transform this "
"model into something that we can simulate.  This simulation step essentially"
" amounts to solving (usually numerically) the equation and providing a "
"solution trajectory like this:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:57
msgid ""
"This gives you the first initial hint at one of the compelling aspects about"
" using a modeling language to describe mathematical behavior.  We didn't "
"need to describe how to solve this differential equation.  The focus is "
"entirely on behavior.  As we work our way through more complex examples, we "
"will see that **much of the tedious work involving the solution process is "
"handled automatically by the Modelica compiler**."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:68
msgid "Adding Some Documentation"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:70
msgid ""
"Now that we've solved this simple mathematical equation, let's turn our "
"attention briefly to how we can make the model a bit more readable.  "
"Consider the following model:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:82
msgid "Note the quoted text in this model."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:84
msgid ""
"It is important to understand that the quoted text blocks, called "
"\"strings\" in computer science, are **not** comments.  They are "
"\"descriptive strings\" and, unlike comments, they cannot be added in "
"arbitrary places.  Instead, they can only be inserted in specific places to "
"provide additional documentation about the elements of the model they are "
"associated with."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:90
msgid ""
"For example, the first string \"A simple first order differential equation\""
" is used to describe what this is a model of.  Note how it follows the name "
"of the model.  If you wish to include such documentation about the model, it"
" must appear immediately after the model name as shown."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:96
msgid ""
"As we will see later, this kind of documentation can be used by tools in "
"many ways.  For example, when searching for models, a tool may use these "
"descriptive strings when identifying matches.  This text may also be "
"associated with a graphical representation of the models.  And, of course, "
"this kind of documentation is very useful for anybody reading the model."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:103
msgid ""
"As this example demonstrates, there are other places that the descriptive "
"text can appear.  For example, it may be included after the declaration of a"
" variable or equation to document them."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:110
msgid "Initialization"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:112
msgid ""
"As we have seen already, Modelica allows us to describe model behavior in "
"terms of differential equations.  But the initial conditions we choose are "
"just as important as the equations."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:116
msgid ""
"For this reason, Modelica also provides constructs for describing the "
"initialization of our system of equations.  For example, if we wanted the "
"initial value of ``x`` in our model to be *2*, we could add an ``initial "
"equation`` section to our model as follows:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:129
msgid ""
"Note that the only difference between this model and the previous one, "
"presented in the section on :ref:`first-order-doc`, is the addition of the "
"``initial equation`` section which contains the equation ``x = 2``.  In the "
"previous example, the initial value of ``x`` at the start of the simulation "
"was unspecified.  Generally speaking, this means that the initial value for "
"``x`` will be the value of its ``start`` attribute (which is zero by "
"default).  However, because each tool uses their own specific algorithms to "
"formulate the final system of equations, it is always best to state initial "
"conditions explicitly, as we have done here.  By adding this equation to the"
" ``initial equation`` section, we are explicitly specifying the initial "
"condition for ``x``."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:142
msgid ""
"As a result, the solution trajectory is quite different as we can see in the"
" following figure:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:147
msgid ""
"The model ``FirstOrderInitial`` shows a typical way of initializing a system"
" by providing explicit initial values for the states of the system.  In "
"fact, a system of differential equations is incomplete without a "
"specification for how the initial conditions are determined. Our "
"``FirstOrderInitial`` model would be represented mathematically as:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:156
msgid ""
"However, there are many cases where you want a more sophisticated type of "
"initialization.  An ``initial equation`` section can contain more than just "
"explicit equations for the initial values of the state variables."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:161
msgid ""
"For example, we might want our initial conditions to be such that the "
"derivative of :math:`x` was zero at the start of the simulation.  In this "
"case, only a bit of trivial algebra is required to realize that this could "
"be accomplished by specifying an initial condition of :math:`x(0)=1`.  "
"However, for more complex systems, it is far from trivial to determine the "
"initial state values that would satisfy such a requirement.  In those cases,"
" it is possible to express the constraint that :math:`\\dot{x}(0)=0` "
"directly in Modelica as follows:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:176
msgid "Simulating this system gives the following solution:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:180
msgid ""
"As we see from these results, the initial derivative of :math:`x` is zero at"
" the start of the simulation and remains zero because there are no external "
"influences acting on this system that would disrupt this equilibrium."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:185
msgid ""
"This provides a glimpse of the initialization capablities in Modelica. More "
"complete coverage of the initialization topic can be found in the "
":ref:`initialization` section later in this chapter."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:192
msgid "Experimental Conditions"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:197
msgid ""
"When building a model, the model developer might wish to associate specific "
"experimental conditions with the model.  This can be done using something "
"called an ``annotation``.  An annotation includes information that is not "
"directly related to the behavior of the model."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:202
msgid ""
"For example, experimental conditions describe information like the start "
"time of the simulation, the stop time, solution tolerance and so on.  This "
"is not information about the behavior of the model itself, but rather "
"information about how to approach simulating that behavior. Experimental "
"conditions are stored in a model using a specific annotation called the "
"``experiment`` annotation."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:209
msgid ""
"There are four pieces of information that can be specified in an experiment "
"annotation.  All of them are optional.  The following is a model of our "
"first order system that includes an experiment annotation:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:219
msgid ""
"The following trajectory was simulated using these experimental conditions:"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:224
msgid ""
"The trajectory terminates at 8 seconds because the simulator used the "
"``experiment`` annotation to determine how long to run the simulation."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:0
msgid "Annotation Support"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:229
msgid ""
"The ``experiment`` annotation is widely supported.  But it is important to "
"keep in mind that, in general, a tool is free to ignore any or all "
"annotations."
msgstr ""

#: ../../source/behavior/equations/first_order.rst:19
msgid "model"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:20
msgid "der"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:21
msgid "Real"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:80
msgid "descriptive strings"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:121
msgid "initial equation"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:194
#: ../../source/behavior/equations/first_order.rst:195
msgid "annotation"
msgstr ""

#: ../../source/behavior/equations/first_order.rst:195
msgid "experiment"
msgstr ""
