Expression 12: "f" Subscript, "r" "x" , Baseline equals negative left parenthesis, sin left parenthesis, "r" Subscript, "z" , Baseline , right parenthesis , right parenthesis left parenthesis, cos left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis minus left parenthesis, sin left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline left parenthesis, sin left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis , right parenthesis plus left parenthesis, left parenthesis, sin left parenthesis, "r" Subscript, "y" , Baseline , right parenthesis , right parenthesis left parenthesis, left parenthesis, sin left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis plus left parenthesis, cos left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "d" , right parenthesis minus left parenthesis, "D" Subscript, "c" , Baseline , right parenthesis sin left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis , right parenthesis plus left parenthesis, cos left parenthesis, "r" Subscript, "y" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" cos left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline cos left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis , right parenthesis left parenthesis, cos left parenthesis, "r" Subscript, "z" , Baseline , right parenthesis , right parenthesisfrx=−sinrzcosrxDsinacosd−Dcsinaccosdc−sinrxDsind−Dcsindc+sinrysinrxDsinacosd−Dcsinaccosdc+cosrxDsind−Dcsindc+cosryDcosacosd−Dccosaccosdccosrz
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12
Expression 13: "f" Subscript, "r" "y" , Baseline equals left parenthesis, cos left parenthesis, "r" Subscript, "z" , Baseline , right parenthesis , right parenthesis left parenthesis, left parenthesis, cos left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis minus left parenthesis, sin left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis , right parenthesis plus left parenthesis, left parenthesis, sin left parenthesis, "r" Subscript, "y" , Baseline , right parenthesis , right parenthesis left parenthesis, left parenthesis, sin left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis plus left parenthesis, cos left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis , right parenthesis plus left parenthesis, cos left parenthesis, "r" Subscript, "y" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" cos left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline cos left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis , right parenthesis left parenthesis, sin left parenthesis, "r" Subscript, "z" , Baseline , right parenthesis , right parenthesisfry=cosrzcosrxDsinacosd−Dcsinaccosdc−sinrxDsind−Dcsindc+sinrysinrxDsinacosd−Dcsinaccosdc+cosrxDsind−Dcsindc+cosryDcosacosd−Dccosaccosdcsinrz
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13
Expression 14: "f" Subscript, "r" "z" , Baseline equals left parenthesis, cos left parenthesis, "r" Subscript, "y" , Baseline , right parenthesis , right parenthesis left parenthesis, left parenthesis, sin left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis plus left parenthesis, cos left parenthesis, "r" Subscript, "x" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" sin left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline sin left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesis , right parenthesis minus left parenthesis, sin left parenthesis, "r" Subscript, "y" , Baseline , right parenthesis , right parenthesis left parenthesis, "D" cos left parenthesis, "a" , right parenthesis cos left parenthesis, "d" , right parenthesis minus "D" Subscript, "c" , Baseline cos left parenthesis, "a" Subscript, "c" , Baseline , right parenthesis cos left parenthesis, "d" Subscript, "c" , Baseline , right parenthesis , right parenthesisfrz=cosrysinrxDsinacosd−Dcsinaccosdc+cosrxDsind−Dcsindc−sinryDcosacosd−Dccosaccosdc
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14
Hidden Label: left parenthesis, "f" Subscript, "x" , Baseline left parenthesis, "X" , "Y" , "Z" , right parenthesis , "f" Subscript, "y" , Baseline left parenthesis, "X" , "Y" , "Z" , right parenthesis , right parenthesisfxX,Y,Z,fyX,Y,Z
Label
15
Expression 16: "X" equals "a" Subscript, 1 , Baseline for "a" Subscript, 1 , Baseline equals left bracket, 1...4 , right bracket , "a" Subscript, 2 , Baseline equals left bracket, 1...4 , right bracket , "a" Subscript, 3 , Baseline equals left bracket, 1...4 , right bracketX=a1fora1=1...4,a2=1...4,a3=1...4
equals=
11
22
33
44
11
22
33
44
11
22
33
44
11
22
33
64 element list
16
Expression 17: "Y" equals "a" Subscript, 2 , Baseline times 10for "a" Subscript, 1 , Baseline equals left bracket, 1...4 , right bracket , "a" Subscript, 2 , Baseline equals left bracket, 1...4 , right bracket , "a" Subscript, 3 , Baseline equals left bracket, 1...4 , right bracketY=a2·10fora1=1...4,a2=1...4,a3=1...4
equals=
1010
1010
1010
1010
2020
2020
2020
2020
3030
3030
3030
3030
4040
4040
4040
64 element list
17
Expression 18: "Z" equals "a" Subscript, 3 , Baseline times 10for "a" Subscript, 1 , Baseline equals left bracket, 1...4 , right bracket , "a" Subscript, 2 , Baseline equals left bracket, 1...4 , right bracket , "a" Subscript, 3 , Baseline equals left bracket, 1...4 , right bracketZ=a3·10fora1=1...4,a2=1...4,a3=1...4