3210force.fodt

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        <mtable>
         <mtr>
          <mtd>
           <mrow>
            <mrow>
             <msub>
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                <mi mathvariant="italic">IeJe</mi>
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        <annotation encoding="StarMath 5.0">t_FIeJe
=
step
left(
r_IeJe , 
r_1-d,
1, 
r_1 , 
0 
right)
left(
k
left(
r_1 - r_IeJe
right)
+ c{dot r}_IeJe
right)

newline
&quot;&quot;~~~~~
+
step
left(
r_IeJe,
r_2 ,
0,
r_2+d,
1
right)
left(
k
left(
r_IeJe - r_2
right)
+ c{dot r}_IeJe
right)
</annotation>
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   <text:h text:style-name="Heading_20_1" text:outline-level="1">General ForceTorque Examples</text:h>
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   <text:p text:style-name="Standard">It is a Parallel z Action-Reaction Torque.</text:p>
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=
step
left(
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r_1-d,
1, 
r_1 , 
0 
right)
left(
k
left(
r_1 - r_IeJeIe3
right)
+ cv_IeJeIe3
right)

newline
&quot;&quot;~~~~~
+
step
left(
r_IeJeIe3,
r_2 ,
0,
r_2+d,
1
right)
left(
k
left(
r_IeJeIe3 - r_2
right)
+ cv_IeJeIe3
right)
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         </mtr>
        </mtable>
        <annotation encoding="StarMath 5.0">T_IeIe3
=
step
left(
%theta_IeJe3z , 
%theta_1-d,
1, 
%theta_1 , 
0 
right)
left(
k
left(
%theta_1 - %theta_IeJe3z
right)
+ c%omega_IeJeIe3
right)

newline
&quot;&quot;~~~~~
+
step
left(
%theta_IeJe3z,
%theta_2 ,
0,
%theta_2+d,
1
right)
left(
k
left(
%theta_IeJe3z - %theta_2
right)
+ c%omega_IeJeIe3
right)
</annotation>
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   <text:p text:style-name="Standard">Can be viewed as an action-reaction force and an action-reaction torque combination.</text:p>
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F_IeIe3
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{bold nitalic %alpha}_LeMeNe,
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matrix
{
F_IeIex ##
F_IeIey ##
F_IeIez ##
T_IeIex ##
T_IeIey ##
T_IeIez
}
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_1" text:outline-level="1">N-body Interaction</text:h>
   <text:p text:style-name="Standard">Can be viewed as a<draw:frame draw:style-name="fr1" draw:name="Object40" text:anchor-type="as-char" svg:width="0.6744in" svg:height="0.4098in" draw:z-index="39"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mfrac>
         <mrow>
          <mi>n</mi>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
            <mrow>
             <mi>n</mi>
             <mo stretchy="false">−</mo>
             <mn>1</mn>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
         </mrow>
         <mn>2</mn>
        </mfrac>
        <annotation encoding="StarMath 5.0">{n(n-1)}
over
2</annotation>
       </semantics>
      </math>
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     </draw:image>
    </draw:frame>action-reaction forceTorque combination.</text:p>
   <text:p text:style-name="Standard">Just need to avoid computing the same quantities repeatedly.</text:p>
   <text:h text:style-name="Heading_20_2" text:outline-level="2">Finite Element Analysis</text:h>
   <text:p text:style-name="Standard">Restrict to interactions of neighbours only.</text:p>
   <text:h text:style-name="Heading_20_2" text:outline-level="2">Lumped Mass Method</text:h>
   <text:p text:style-name="Standard">Restrict to interactions of neighbours only.</text:p>
   <text:p text:style-name="P1"/>
   <text:h text:style-name="Heading_20_2" text:outline-level="2"/>
  </office:text>
 </office:body>
</office:document>