7000euler.fodt

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   <text:h text:style-name="Heading_20_2" text:outline-level="2">Euler Parameter Constraint,<draw:frame draw:style-name="fr1" draw:name="Object8" text:anchor-type="as-char" svg:width="0.2756in" svg:height="0.2165in" draw:z-index="8"><draw:object>
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        <annotation encoding="StarMath 5.0">left[{bold nitalic B}right]left[{bold nitalic B}right]^T
=
left [
matrix
{
E_4 # -E_3 # E_2 # -E_1 ##
E_3 # E_4 # -E_1 # -E_2 ##
-E_2 # E_1 # E_4 # -E_3
}
right ]
left [
matrix
{
E_4 # E_3 # -E_2 ##
-E_3 # E_4 # E_1 ##
E_2 # -E_1 # E_4 ##
-E_1 # -E_2 # -E_3
}
right ]
=
left [
matrix
{
1 # 0 # 0 ##
0 # 1 # 0 ##
0 # 0 # 1
}
right ]
</annotation>
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        <annotation encoding="StarMath 5.0">left[{bold nitalic C}right]^T left[{bold nitalic C}right]
=
left [
matrix
{
E_4 # -E_3 # E_2 ##
E_3 # E_4 # -E_1 ##
-E_2 # E_1 # E_4 ##
-E_1 # -E_2 # -E_3
}
right ]
left [
matrix
{
E_4 # E_3 # -E_2 # -E_1 ##
-E_3 # E_4 # E_1 # -E_2 ##
E_2 # -E_1 # E_4 # -E_3
}
right ]
=
left [
matrix
{
1-E_1 E_1 # -E_1 E_2 # -E_1 E_3 # -E_1 E_4 ##
-E_2 E_1 # 1-E_2 E_2 # -E_2 E_3 # -E_2 E_4 ##
-E_3 E_1 # -E_3 E_2 # 1-E_3 E_3 # -E_3 E_4 ##
-E_4 E_1 # -E_4 E_2 # -E_4 E_3 # 1-E_4 E_4
}
right ]
</annotation>
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        <annotation encoding="StarMath 5.0">&quot;&quot;
left[
{bold nitalic A}
right]_Oo
=
left[
{bold nitalic B}
right]
left[
{bold nitalic C}
right]^T

newline
&quot;&quot;~~~~~~
=
left [
matrix
{
E_4 # -E_3 # E_2 # -E_1 ##
E_3 # E_4 # -E_1 # -E_2 ##
-E_2 # E_1 # E_4 # -E_3
}
right ]
left [
matrix
{
E_4 # -E_3 # E_2 ##
E_3 # E_4 # -E_1 ##
-E_2 # E_1 # E_4 ##
-E_1 # -E_2 # -E_3
}
right ]

newline
&quot;&quot;~~~~~~
=
left [
matrix
{
E^2_1-E^2_2-E^2_3+E^2_4 
# 
2 left(E_1E_2-E_3E_4 right) 
# 
2 left(E_1E_3+E_2E_4 right) 
##
2 left(E_1E_2+E_3E_4 right) 
# 
-E^2_1+E^2_2-E^2_3+E^2_4 
# 
2 left(E_2E_3-E_1E_4 right) 
##
2 left(E_1E_3-E_2E_4 right) 
# 
2 left(E_2E_3+E_1E_4 right) 
# 
-E^2_1-E^2_2+E^2_3+E^2_4 
}
right ]
</annotation>
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~~
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~~
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=
left(
A_13+A_31
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over
{4E_3}
~~
E_2
=
left(
A_23+A_32
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over
{4E_3}
~~
E_4
=
left(
A_21-A_12
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over
{4E_3}
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