2020kineij.fodt

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over
{partial {bold nitalic %alpha}}
=
1 over {r_IeJe}
{partial {bold nitalic r}^T_IeJeO}
over
{partial {bold nitalic %alpha}}
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Partial Derivative of<draw:frame draw:style-name="fr1" draw:name="Object192" text:anchor-type="as-char" svg:width="0.3299in" svg:height="0.2165in" draw:z-index="14"><draw:object>
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        <annotation encoding="StarMath 5.0">{partial^2 r_IeJe}
over
{partial {bold nitalic %alpha}partial {bold nitalic %beta}}
=
-{
1 over {r^2_IeJe}}
{partial {bold nitalic r}^T_IeJeO}
over
{partial {bold nitalic %alpha}}
{bold nitalic r}_IeJeO
{partial r_IeJe}
over
{partial {bold nitalic %beta}}
+
1 over {r_IeJe}
{partial^2 {bold nitalic r}^T_IeJeO}
over
{partial {bold nitalic %alpha}partial {bold nitalic %beta}}
{bold nitalic r}_IeJeO
+
1 over {r_IeJe}
{partial {bold nitalic r}^T_IeJeO}
over
{partial {bold nitalic %alpha}}
{partial {bold nitalic r}_IeJeO}
over
{partial {bold nitalic %beta}}
</annotation>
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left(
t,
{bold nitalic q}_I,{bold nitalic s}_I,
{bold nitalic q}_J,{bold nitalic s}_J,
{bold nitalic v}_I,{bold nitalic dot s}_I,
{bold nitalic v}_J,{bold nitalic dot s}_J
right)</annotation>
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        <annotation encoding="StarMath 5.0">{dot r}_IeJe
=
{dr_IeJe}
over
{dt}
=
1 over {r_IeJe}
{d{bold nitalic r}^T_IeJeO}
over
{dt}
{bold nitalic r}_IeJeO
=
1 over {r_IeJe}
{bold nitalic v}^T_IeJeO
{bold nitalic r}_IeJeO

</annotation>
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left(
1 over {r_IeJe}
{bold nitalic v}^T_IeJeO
{bold nitalic r}_IeJeO
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{bold nitalic r}_IeJeO
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=
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{bold nitalic r}_IeJeO
+
{bold nitalic v}^T_IeJeO
{bold nitalic v}_IeJeO
-
{dot r}^2_IeJe
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{partial {r}_IeJe}
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{dot r}^2_IeJe
right)

newline
&quot;&quot;~~~~~~~
+
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2
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                <mi mathvariant="italic">IeJeO</mi>
               </msub>
              </mrow>
              <mrow>
               <mo stretchy="false">∂</mo>
               <mstyle mathvariant="bold">
                <mi mathvariant="normal">α</mi>
               </mstyle>
              </mrow>
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               <mi mathvariant="normal">v</mi>
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            <mrow>
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                <mover accent="true">
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             <mo stretchy="false">−</mo>
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            </mrow>
            <mfrac>
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        </mrow>
        <annotation encoding="StarMath 5.0">{partial {ddot  r}_IeJe}
over
{partial {bold nitalic %alpha}}
=
1 over {r_IeJe}
left(
{partial {bold nitalic a}^T_IeJeO}
over
{partial {bold nitalic %alpha}}
{bold nitalic r}_IeJeO
+
{bold nitalic a}^T_IeJeO
{partial {bold nitalic r}_IeJeO}
over
{partial {bold nitalic %alpha}}

+
2
{partial {bold nitalic v}^T_IeJeO}
over
{partial {bold nitalic %alpha}}
{bold nitalic v}_IeJeO
-
2
{dot r}_IeJe
{partial {dot  r}_IeJe}
over
{partial {bold nitalic %alpha}}
-
{ddot r}_IeJe
{partial {r}_IeJe}
over
{partial {bold nitalic %alpha}}
right)

</annotation>
       </semantics>
      </math>
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