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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Euler Parameter Constraint,<draw:frame draw:style-name="fr1" draw:name="Object27" text:anchor-type="as-char" svg:width="0.5819in" svg:height="0.2417in" draw:z-index="7"><draw:object>
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left(
{bold nitalic q}_E
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+
E^2_{2}
+
E^2_{3}
+
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- 1
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over
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=
left[
matrix
{
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0 # 2 # 0 # 0 ##
0 # 0 # 2 # 0 ##
0 # 0 # 0 # 2 
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right]
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">DistanceIeJe Constraint<draw:frame draw:style-name="fr1" draw:name="Object51" text:anchor-type="as-char" svg:width="0.902in" svg:height="0.2299in" draw:z-index="14"><draw:object>
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left(
t,
{bold nitalic q},
{bold nitalic s}
right)
</annotation>
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          </msub>
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         </mrow>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_IeJe
=
r_IeJe
-
f(t)
=
0</annotation>
       </semantics>
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   <text:h text:style-name="Heading_20_4" text:outline-level="4">Partial Derivative of<draw:frame draw:style-name="fr1" draw:name="Object53" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="16"><draw:object>
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</annotation>
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=
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=
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over
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   <text:h text:style-name="Heading_20_4" text:outline-level="4">Partial Derivative of<draw:frame draw:style-name="fr1" draw:name="Object74" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="37"><draw:object>
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   <text:h text:style-name="Heading_20_4" text:outline-level="4">Partial Derivative of<draw:frame draw:style-name="fr1" draw:name="Object82" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="45"><draw:object>
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            </msup>
            <msub>
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            </msub>
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        <annotation encoding="StarMath 5.0">{partial^2 G_IeJe}
over
{partial t^2}
=
{partial^2 r_IeJe}
over
{partial t^2}
-
{partial^2 f(t)}
over
{partial t^2}
</annotation>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">DistanceIeJe Constraint alternative<draw:frame draw:style-name="fr1" draw:name="Object28" text:anchor-type="as-char" svg:width="0.95in" svg:height="0.2299in" draw:z-index="73"><draw:object>
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         </msub>
         <mrow>
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            </mstyle>
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            <mstyle mathvariant="bold">
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            </mstyle>
           </mrow>
          </mrow>
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         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_IeJe2
left(
t,
{bold nitalic q},
{bold nitalic s}
right)
</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       <semantics>
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         <mrow>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
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           <mi>T</mi>
          </msubsup>
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         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
          </msub>
          <mo stretchy="false">−</mo>
          <msup>
           <mi>f</mi>
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          </msup>
         </mrow>
         <mrow>
          <mrow>
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          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_IeJe2
=
{bold nitalic r}^T_IeJeO
{bold nitalic r}_IeJeO
-
f^2(t)
=
0</annotation>
       </semantics>
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   <text:h text:style-name="Heading_20_4" text:outline-level="4">Partial Derivative of<draw:frame draw:style-name="fr1" draw:name="Object39" text:anchor-type="as-char" svg:width="0.4299in" svg:height="0.2165in" draw:z-index="88"><draw:object>
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=
r_IeJeIexy
-
f(t)
=
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left(
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right)
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=
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{bold nitalic r}_IeJeIexy
-
f^2(t)
=
0</annotation>
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   <text:h text:style-name="Heading_20_4" text:outline-level="4">Partial Derivative of<draw:frame draw:style-name="fr1" draw:name="Object93" text:anchor-type="as-char" svg:width="0.5929in" svg:height="0.2165in" draw:z-index="133"><draw:object>
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=
r_IeJeOi
-
f(t)
=
0</annotation>
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   <text:p text:style-name="equation">Derivatives are similar to<draw:frame draw:style-name="fr1" draw:name="Object143" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="149"><draw:object>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">DisplacementIeJeKei Component Constraint<draw:frame draw:style-name="fr1" draw:name="Object86" text:anchor-type="as-char" svg:width="1.0362in" svg:height="0.2299in" draw:z-index="49"><draw:object>
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=
r_IeJeKei
-
f(t)
=
0</annotation>
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    </draw:frame></text:p>
   <text:p text:style-name="equation">Derivatives are similar to<draw:frame draw:style-name="fr1" draw:name="Object11" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="64"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
         <mi>G</mi>
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</annotation>
       </semantics>
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     </draw:image>
    </draw:frame>above. <text:span text:style-name="T1">Don&apos;t forget the endframe K.</text:span></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Direction Cosine Constraint<draw:frame draw:style-name="fr1" draw:name="Object9" text:anchor-type="as-char" svg:width="0.8638in" svg:height="0.2299in" draw:z-index="53"><draw:object>
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          <mi>G</mi>
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          <mo fence="true" form="prefix" stretchy="true">(</mo>
          <mrow>
           <mrow>
            <mi>t</mi>
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        <annotation encoding="StarMath 5.0">G_&quot;cos&quot;
left(
t,
{bold nitalic q},
{bold nitalic s}
right)
</annotation>
       </semantics>
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     </draw:object><draw:image>
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   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object10" text:anchor-type="as-char" svg:width="2.5516in" svg:height="0.2299in" draw:z-index="54"><draw:object>
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left(
t,
{bold nitalic q},
{bold nitalic s}
right)
=
A_IeiJej
left(
t,
{bold nitalic q},
{bold nitalic s}
right) 
- 
f(t)
=
0</annotation>
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   <text:p text:style-name="equation">Derivatives are similar to<draw:frame draw:style-name="fr1" draw:name="Object12" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="56"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
         <mi>G</mi>
         <mi mathvariant="italic">IeJe</mi>
        </msub>
        <annotation encoding="StarMath 5.0">G_IeJe
</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
      <office:binary-data>VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAcUDAAAn
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     </draw:image>
    </draw:frame>above.</text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Bryant Angle x Constraint<draw:frame draw:style-name="fr1" draw:name="Object137" text:anchor-type="as-char" svg:width="0.9055in" svg:height="0.2299in" draw:z-index="143"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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         </msub>
         <mrow>
          <mo fence="true" form="prefix" stretchy="true">(</mo>
          <mrow>
           <mrow>
            <mi>t</mi>
            <mi>,</mi>
            <mstyle mathvariant="bold">
             <mi mathvariant="normal">q</mi>
            </mstyle>
            <mi>,</mi>
            <mstyle mathvariant="bold">
             <mi mathvariant="normal">s</mi>
            </mstyle>
           </mrow>
          </mrow>
          <mo fence="true" form="postfix" stretchy="true">)</mo>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_bryx
left(
t,
{bold nitalic q},
{bold nitalic s}
right)
</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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   <text:p text:style-name="equation">Derivatives are similar to<draw:frame draw:style-name="fr1" draw:name="Object139" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="145"><draw:object>
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=
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- 
f(t)
=
0</annotation>
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   <text:p text:style-name="equation">Derivatives are similar to<draw:frame draw:style-name="fr1" draw:name="Object142" text:anchor-type="as-char" svg:width="0.3799in" svg:height="0.2165in" draw:z-index="148"><draw:object>
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