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#: ../../source/components/components/rot_comps_basic.rst:4
msgid "Basic Rotational Components"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:6
msgid ""
"In this section, we'll show how to create basic components for modeling one-"
"dimensional rotational systems.  We'll build on our discussion of rotational"
" connectors and show how they can be used to define the interfaces for basic"
" rotational components.  Finally, we'll show how those rotational components"
" can then be assembled into a system model that replicates the behavior of "
"the equation-based version of the same system presented in the first "
"chapter."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:15
msgid "Component Models"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:17
msgid ""
"In the first chapter, we considered :ref:`mech-example` modeled strictly in "
"terms of equations (*i.e.,* without component models).  In this section, we "
"will start by recreating that system model using components.  To do this, we"
" first have to define models for the fundamental components we require.  "
"These will consist of models for an inertia, a spring, a damper and a "
"mechanical ground."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:24
msgid ""
"As in :ref:`the previous section<electrical-components>`, we will first "
"define the component models using verbose formulations and then we will "
"revisit these definitions and attempt to factor out common code to avoid "
"repetition across component models."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:30
msgid "Coordinate Systems"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:32
msgid ""
"The method for creating these models will be very similar to how we "
"previously created component models in the heat transfer and electrical "
"domains.  But before we start building component models, we should first "
"discuss one of the complexities associated with mechanical systems, "
"coordinate systems."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:38
msgid ""
"In the mechanical domain, the conserved quantity we will be tracking is "
"momentum.  What makes momentum different from the conserved quantities we've"
" already covered, heat and charge, is that it is directional.  Since we are "
"only concerning ourselves with the one dimensional case here, the "
"consequence of this directionality is that momentum is a signed quantity "
"(*i.e.,* it can be positive or negative)."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:50
msgid ""
"Consider a rotating mass with a moment of inertia, :math:`J`.  If the "
"angular position of the inertia is represented by :math:`\\varphi`, then the"
" angular velocity of the inertia, :math:`\\omega`, is defined as:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:59
msgid ""
"Obviously, a positive value of :math:`\\omega` will result in an increase in"
" :math:`\\varphi` over time.  Furthermore, the angular acceleration of the "
"inertia, :math:`\\alpha`, is defined as:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:67
msgid ""
"As with the angular velocity, we can see that a positive value for "
":math:`\\alpha` will result in an increase in the angular velocity. Finally,"
" the angular momentum of this rotating inertia is defined as :math:`J "
"\\omega` and we know from Euler's laws of motion that (assuming J is a "
"constant):"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:77
msgid ""
"From this relationship, it is clear that a positive value for the torque, "
":math:`\\tau`, will increase the amount of momentum stored in the mass."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:81
msgid ""
"The point of presenting all these relationships is to underscore the sign "
"conventions associated with :math:`\\varphi`, :math:`\\omega`, "
":math:`\\alpha` and :math:`\\tau`.  They are all tied to the fundamental "
"definition of what a positive angular position is.  **Whatever direction "
"causes** :math:`\\varphi` **to increase is the same direction that "
"corresponds to a positive velocity, a positive acceleration and a positive "
"torque**."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:90
#: ../../source/components/components/rot_comps_basic.rst:247
msgid "Rotational Inertia"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:92
msgid ""
"With this discussion about sign conventions and coordinate systems out of "
"the way, we can start creating our component models.  We'll start with the "
"inertia model:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:100
msgid ""
"The ``Inertia`` model includes two \"flanges\", one on either end.  The "
"significance of these flanges is made clearer from the icon of the "
"``Inertia`` model:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:108
msgid ""
"In other words, the ``Inertia`` model includes a flange on either end. You "
"can think of this model as a shaft with connectors on either end."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:111
msgid ""
"Now, the fundamental equation we wish to capture in the ``Inertia`` model "
"is:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:118
msgid ""
"This is basically expressing the fact that the increase in momentum stored "
"within the inertia is equal to the sum of the torques applied to the "
"inertia. Recall, from our previous discussions on :ref:`acausal-"
"connections`, that the sign convention for flow variables on connectors "
"(``flange_a.tau`` and ``flange_b.tau`` in this case) is that a positive "
"value represents a flow of the conserved quantity into the component model."
"  The fact that ``flange_a`` and ``flange_b`` have the same sign convention "
"means that the ``Inertia`` model is symmetric (*i.e.,* it can be flipped "
"over and it doesn't change the behavior)."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:129
msgid ""
"However, this equation refers to the internal variables ``w`` (which "
"represents :math:`\\omega`) and ``tau`` so we need to include declarations "
"and definitions for those variables as well."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:134
#: ../../source/components/components/rot_comps_basic.rst:257
msgid "Spring Model"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:136
msgid "Next, let us consider the definition of a spring model:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:142
msgid "The icon for our spring model is rendered as:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:148
msgid ""
"Like the ``Inertia`` model, the ``Spring`` model has two connectors, one on "
"each end.  It also defines many of the same internal variables.  Ultimately,"
" the behavior of the spring comes down to this equation:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:157
msgid ""
"In fact, apart from this equation and the parameter ``c``, much of the "
"content in the ``Spring`` model is the same as the content in the "
"``Inertia`` model."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:162
#: ../../source/components/components/rot_comps_basic.rst:267
msgid "Damper Model"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:164
msgid ""
"The ``Damper`` model is also very similar to the ``Spring`` model. Again, "
"the main differences are the parameter (``d`` in this case) and one "
"equation:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:173
msgid "The icon for the ``Damper`` model is rendered as:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:182
msgid "DRY Component Models"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:184
msgid ""
"We already have models for an inertia, a spring and a damper.  The only "
"model we are missing in order to complete our :ref:`dual spring mass damper "
"system<mech-example>` is a model of mechanical ground. But before we "
"complete that model, let's take a moment to revisit the models we've already"
" created with the goal of factoring out the large amount of code shared "
"between these models.  As in :ref:`the previous section<electrical-"
"components>`, let's take the time to apply the DRY (Don't Repeat Yourself) "
"principle."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:194
msgid "Common Code"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:196
msgid ""
"It is worth noting that because the Modelica Standard Library has an "
"extensive collection of rotational components, it was forced to deal with "
"this issue of redundant code almost from the start.  However, we will not be"
" using the ``partial`` models from the Modelica Standard Library here simply"
" because they are designed to deal with many other cases that are not "
"relevant in this context.  As a result, it's complexity (although necessary)"
" makes it unsuitable pedagogically."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:204
msgid ""
"But one thing we will preserve from the Modelica Standard Library is the "
"need for multiple ``partial`` models.  This need arises from the fact that, "
"unlike in our previous discussion of :ref:`electrical-components`, our "
"rotational component models share different amounts of code with each other."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:210
msgid ""
"What is common to all of our models is the existence of two flange "
"connectors, ``flange_a`` and ``flange_b``.  However, while the ``Inertia`` "
"model has the capacity to store angular momentum, the ``Spring`` and "
"``Damper`` models do not.  As a result, the conservation equations are "
"different among these components."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:216
msgid ""
"Let's start with the elements that are common to all three models. These are"
" represented by the following ``TwoFlange`` model:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:222
msgid ""
"In addition to defining the two flanges, ``flange_a`` and ``flange_b``, this"
" model also defines the relative angle between these flanges, *i.e.,* "
"``phi_rel``.  Of course, this model is also marked as ``partial`` since it "
"is missing any description of the component's behavior."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:228
msgid ""
"We could have all three models inherit from this model.  But then we would "
"still have some redundant equations between our ``Spring`` and ``Damper`` "
"model.  So we will instead create a slightly more specialized version of the"
" ``TwoFlange`` model to represent compliant models that do not store "
"momentum:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:237
msgid ""
"The ``Compliant`` model adds on additional internal variable (to represent "
"the torque that passes through the component from ``flange_a`` to "
"``flange_b``) and an equation indicating that no angular momentum is stored "
"by the component."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:242
msgid ""
"With these base classes defined, let us quickly revisit the various "
"component model definitions to see how much more succinct they can be made "
"by using inheritance."
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:249
msgid ""
"Leveraging the ``TwoFlanges`` model, our ``Inertia`` model can be simplified"
" to:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:259
msgid ""
"In the same way, inheriting from the ``Compliant`` model our ``Spring`` "
"model can be much more compactly represented as:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:269
msgid "Likewise, the ``Damper`` model is similarly simplified:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:276
msgid "Mechanical Ground"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:278
msgid ""
"Finally, we can complete the one model remaining in order to complete our "
":ref:`dual spring mass damper system<mech-example>`.  The mechanical ground "
"model is defined as follows:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:287
msgid "Dual Spring Mass Damper System"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:289
msgid ""
"Finally, we have all the parts we need in order to reconstruct the example "
"we saw in the first chapter.  Using the various components already defined "
"in this section, the Modelica code for our component based system model "
"looks like this:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:297
msgid "The diagram for this model, when rendered, looks like this:"
msgstr ""

#: ../../source/components/components/rot_comps_basic.rst:307
msgid ""
"This completes our discussion of basic rotational components.  But there is "
"quite a bit more to say about rotational components in the next section on "
":ref:`adv-rotational-components`."
msgstr ""
