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   <text:h text:style-name="Heading_20_1" text:outline-level="1">Prescribed Path Motion (Preferred)</text:h>
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left(
s
right)</annotation>
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    </draw:frame>where s is a parameter. </text:p>
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    </draw:frame>is path distance.</text:p>
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=
sqrt
{
dx^2 + dy^2 + dz^2
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=
int from -1 to s
sqrt
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over
ds
right)^2 
+ 
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dy
over
ds
right)^2 
+ 
left(
dz
over
ds
right)^2 
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   <text:p text:style-name="Standard">Motion is defined by<draw:frame draw:style-name="fr1" draw:name="Object5" text:anchor-type="as-char" svg:width="0.3409in" svg:height="0.2102in" draw:z-index="5"><draw:object>
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         </mover>
         <mrow>
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          <mrow>
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         </mrow>
        </mrow>
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left(
t
right)</annotation>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Path Distance Constraint<draw:frame draw:style-name="fr1" draw:name="Object6" text:anchor-type="as-char" svg:width="0.6in" svg:height="0.2272in" draw:z-index="6"><draw:object>
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        <annotation encoding="StarMath 5.0">G_{bar s}
left(
s,t
right)</annotation>
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left(
s,t
right)
=
bar s
left(
s
right)
-
bar s
left(
t
right)
=
0


</annotation>
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over
{partial s^2}
=
{partial^2 bar s}
over
{partial s^2}


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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="Object15" text:anchor-type="as-char" svg:width="0.2583in" svg:height="0.2165in" draw:z-index="11"><draw:object>
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over
{partial s partial 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="Object19" text:anchor-type="as-char" svg:width="0.2583in" svg:height="0.2165in" draw:z-index="12"><draw:object>
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{partial t^2}
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-
{
{partial^2 bar s}
over
{partial t^2}
}

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s
right)</annotation>
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left(
s
right)</annotation>
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            </mrow>
           </msqrt>
          </mrow>
         </mrow>
         <mi mathvariant="italic">ds</mi>
        </mrow>
        <annotation encoding="StarMath 5.0">bar s
=
int from s_0 to s
sqrt
{
r^2_x sin^2 left(s right)
+ 
r^2_y cos^2 left(s right)
}
ds</annotation>
       </semantics>
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