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   <text:h text:style-name="P5" text:outline-level="1">Lagrange Equations of the Second Kind</text:h>
   <text:p text:style-name="P1">The basis of this multibody dynamics formulation is the Lagrange Equations of the second kind:</text:p>
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           <mi mathvariant="italic">dt</mi>
          </mfrac>
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           </munderover>
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        <annotation encoding="StarMath 5.0">{dp_{i_q} over dt}
-
{partial T} 
over 
{partial q}_{i_q}
-
Q_{i_q}
-
sum from{i_G=1} to{n_G}
{
{partial { G}_{i_G}} 
over 
{partial q}_{i_q}
{%lambda}_{i_G}
}
-
sum from{i_ bar G=1} to{n_bar G}
{{bar G}_{i_bar G}}
{bar %lambda}_{i_bar G}
=
 0
 ~~~~~~~~
 {i_q}=1,dotsaxis, n_q</annotation>
       </semantics>
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   <text:p text:style-name="P1">The terms in the equations will be defined and derived below.</text:p>
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    </draw:frame>form the Cartesian Frame in inertial frame.</text:p>
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   <text:h text:style-name="P5" text:outline-level="1">Assembly Frame</text:h>
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    </draw:frame>form the Cartesian Frame in assembly frame.</text:p>
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   <text:h text:style-name="P5" text:outline-level="1">Principal Part Frame</text:h>
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   <text:h text:style-name="Heading_20_4" text:outline-level="4">Euler Parameter Constraint,<draw:frame draw:style-name="fr1" draw:name="Object22" text:anchor-type="as-char" svg:width="0.278in" svg:height="0.2138in" draw:z-index="75"><draw:object>
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   <text:h text:style-name="Heading_20_4" text:outline-level="4">Euler Parameter Matrices,<draw:frame draw:style-name="fr1" draw:name="Object24" text:anchor-type="as-char" svg:width="0.5965in" svg:height="0.2134in" draw:z-index="77"><draw:object>
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right rbrace
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right rbrace
~~~~
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right rbrace
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right rbrace
~~~~
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right rbrace
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