- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2017-06-19 17:52:29+12:00
- Desc:
- rearranging equations
- Permanent Source URI:
- https://models.fieldml.org/workspace/43b/rawfile/aa5ad5c54b6b30991f5ce3367468833a49f4531b/BG Tutorial Mechanical Systems/Mechanics 3.cellml
<?xml version='1.0'?>
<model name="aero" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="radian_per_s">
<unit units="radian"/>
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_m">
<unit units="joule"/>
<unit exponent="-1" units="metre"/>
</units>
<units name="m_per_s">
<unit units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="m_per_s2">
<unit units="metre"/>
<unit exponent="-2" units="second"/>
</units>
<units name="m2_per_J">
<unit exponent="2" units="metre"/>
<unit exponent="-1" units="joule"/>
</units>
<units name="Js_per_m2">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="J_per_m2">
<unit units="joule"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="Js2_per_m2">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-2" units="metre"/>
</units>
<component name="main">
<variable initial_value="0" name="t" units="second"/>
<variable initial_value="1" name="r0" units="metre"/>
<!-- State variables-->
<variable initial_value="1" name="theta" units="radian"/>
<variable name="omega" units="radian_per_s"/>
<variable initial_value="4.905" name="q1" units="metre"/>
<variable initial_value="-10" name="v1" units="m_per_s"/>
<variable initial_value="0" name="v2" units="m_per_s"/>
<!-- Constitutive parameters-->
<variable initial_value="9.81" name="g" units="m_per_s2"/>
<variable initial_value="200" name="E1" units="J_per_m2"/>
<variable initial_value="0.1" name="R1" units="Js_per_m2"/>
<variable initial_value="100" name="M1" units="Js2_per_m2"/>
<variable name="u3" units="J_per_m"/>
<!-- Equations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>omega</ci>
<apply>
<divide/>
<ci>v2</ci>
<apply>
<plus/>
<ci>r0</ci>
<ci>q1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u3</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>E1</ci>
<apply>
<plus/>
<ci>q1</ci>
<apply>
<abs/>
<ci>q1</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>theta</ci>
</apply>
<ci>omega</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q1</ci>
</apply>
<ci>v1</ci>
</apply>
<!-- ode(v1, t) = (r0+q1)*omega*omega-(E1*q1+R1*v1)/M1+g*cos(theta);-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v1</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci>r0</ci>
<ci>q1</ci>
</apply>
<ci>omega</ci>
<ci>omega</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>u3</ci>
<apply>
<times/>
<ci>R1</ci>
<ci>v1</ci>
</apply>
</apply>
<ci>M1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g</ci>
<apply>
<cos/>
<ci>theta</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>omega</ci>
</apply>
<ci>v1</ci>
</apply>
<apply>
<times/>
<ci>g</ci>
<apply>
<sin/>
<ci>theta</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>
