- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-01-24 14:52:46+13:00
- Desc:
- correct links to cellml models and remove old docs.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/aed/rawfile/d4accf8429dbf5bdd5dfa1719790f361f5baddbe/FAIRDO BG example 3.1.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="BG1" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- Bond graph model of electrical circuit -->
<units name="J_per_C">
<unit units="joule"/>
<unit exponent="-1" units="coulomb"/>
</units>
<units name="C_per_s">
<unit units="coulomb"/>
<unit exponent="-1" units="second"/>
</units>
<units name="C_per_s2">
<unit units="coulomb"/>
<unit exponent="-2" units="second"/>
</units>
<units name="C2_per_J">
<unit exponent="2" units="coulomb"/>
<unit exponent="-1" units="joule"/>
</units>
<units name="Js_per_C2">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-2" units="coulomb"/>
</units>
<units name="Js2_per_C2">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-2" units="coulomb"/>
</units>
<component name="main">
<variable initial_value="0" name="t" units="second"/>
<!-- State variables-->
<variable initial_value="1" name="q_C" units="coulomb"/>
<!-- charge on capacitor-->
<variable name="v_C" units="C_per_s"/>
<!-- current through capacitor-->
<variable name="v_R" units="C_per_s"/>
<!-- current through resistor-->
<variable initial_value="0" name="v_L" units="C_per_s"/>
<!-- current through inductor-->
<variable name="a_L" units="C_per_s2"/>
<!-- rate of change of current through inductor-->
<variable name="u_C" units="J_per_C"/>
<!-- potential on capacitor-->
<variable name="u_R" units="J_per_C"/>
<!-- potential across resistor-->
<variable name="u_L" units="J_per_C"/>
<!-- potential across inductor-->
<!-- Constitutive parameters-->
<variable initial_value="20" name="C" units="C2_per_J"/>
<!-- capacitance-->
<variable initial_value="2" name="R" units="Js_per_C2"/>
<!-- resistance-->
<variable initial_value="10" name="L" units="Js2_per_C2"/>
<!-- inductance-->
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_C</ci>
</apply>
<ci>v_C</ci>
</apply>
<!-- eqn 3.1.5-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_L</ci>
</apply>
<ci>a_L</ci>
</apply>
<!-- eqn 3.1.7-->
<apply>
<eq/>
<ci>v_C</ci>
<apply>
<minus/>
<ci>v_R</ci>
</apply>
</apply>
<!-- eqn 3.1.1-->
<apply>
<eq/>
<ci>v_R</ci>
<ci>v_L</ci>
</apply>
<!-- eqn 3.1.2-->
<apply>
<eq/>
<ci>u_C</ci>
<apply>
<plus/>
<ci>u_R</ci>
<ci>u_L</ci>
</apply>
</apply>
<!-- eqn 3.1.3-->
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>u_C</ci>
<apply>
<divide/>
<ci>q_C</ci>
<ci>C</ci>
</apply>
</apply>
<!-- eqn 3.1.4-->
<apply>
<eq/>
<ci>u_R</ci>
<apply>
<times/>
<ci>v_R</ci>
<ci>R</ci>
</apply>
</apply>
<!-- eqn 3.1.8-->
<apply>
<eq/>
<ci>u_L</ci>
<apply>
<times/>
<ci>a_L</ci>
<ci>L</ci>
</apply>
</apply>
</math>
<!-- eqn 3.1.6-->
</component>
</model>
