Expression 19: "P" left parenthesis, "x" , "y" , "z" , right parenthesis equals left parenthesis, negative "x" sin left parenthesis, phi Subscript, 0 , Baseline , right parenthesis plus "y" cos left parenthesis, phi Subscript, 0 , Baseline , right parenthesis , negative "x" sin left parenthesis, theta Subscript, 0 , Baseline , right parenthesis cos left parenthesis, phi Subscript, 0 , Baseline , right parenthesis minus "y" sin left parenthesis, theta Subscript, 0 , Baseline , right parenthesis sin left parenthesis, phi Subscript, 0 , Baseline , right parenthesis plus "z" cos left parenthesis, theta Subscript, 0 , Baseline , right parenthesis , right parenthesisPx,y,z=−xsinϕ0+ycosϕ0,−xsinθ0cosϕ0−ysinθ0sinϕ0+zcosθ0
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Plot (show/hide)
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Second plot (show/hide)
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Parametric plot (show/hide)
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Rule for parametrisation σ
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Expression 32: sigma Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis equals StartFraction, negative 2 Over 15 , EndFraction cosine left parenthesis, "u" , right parenthesis left parenthesis, left parenthesis, 3cos left parenthesis, "v" , right parenthesis minus 30sin left parenthesis, "u" , right parenthesis plus 90 left parenthesis, cos left parenthesis, "u" , right parenthesis , right parenthesis to the 4th power sin left parenthesis, "u" , right parenthesis minus 60 left parenthesis, cos left parenthesis, "u" , right parenthesis , right parenthesis to the 6th power sin left parenthesis, "u" , right parenthesis plus 5cos left parenthesis, "u" , right parenthesis cos left parenthesis, "v" , right parenthesis sin left parenthesis, "u" , right parenthesis , right parenthesis , right parenthesisσ1u,v=−215cosu3cosv−30sinu+90cosu4sinu−60cosu6sinu+5cosucosvsinu
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Expression 33: sigma Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis equals negative StartFraction, 1 Over 15 , EndFraction sine left parenthesis, "u" , right parenthesis left parenthesis, 3cos left parenthesis, "v" , right parenthesis minus 3cos squared left parenthesis, "u" , right parenthesis cos left parenthesis, "v" , right parenthesis minus 48 left parenthesis, cos left parenthesis, "u" , right parenthesis , right parenthesis to the 4th power cos left parenthesis, "v" , right parenthesis plus 48 left parenthesis, cos left parenthesis, "u" , right parenthesis , right parenthesis to the 6th power cos left parenthesis, "v" , right parenthesis minus 60sin left parenthesis, "u" , right parenthesis plus 5cos left parenthesis, "u" , right parenthesis cos left parenthesis, "v" , right parenthesis sin left parenthesis, "u" , right parenthesis minus 5 left parenthesis, cos left parenthesis, "u" , right parenthesis , right parenthesis cubed cos left parenthesis, "v" , right parenthesis sin left parenthesis, "u" , right parenthesis minus 80 left parenthesis, cos left parenthesis, "u" , right parenthesis , right parenthesis to the 5th power cos left parenthesis, "v" , right parenthesis sin left parenthesis, "u" , right parenthesis plus 80 left parenthesis, cos left parenthesis, "u" , right parenthesis , right parenthesis to the 7th power cos left parenthesis, "v" , right parenthesis sin left parenthesis, "u" , right parenthesis , right parenthesisσ2u,v=−115sinu3cosv−3cos2ucosv−48cosu4cosv+48cosu6cosv−60sinu+5cosucosvsinu−5cosu3cosvsinu−80cosu5cosvsinu+80cosu7cosvsinu
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Expression 34: sigma Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesis equals StartFraction, 2 Over 15 , EndFraction left parenthesis, 3 plus 5cos left parenthesis, "u" , right parenthesis sin left parenthesis, "u" , right parenthesis , right parenthesis sine left parenthesis, "v" , right parenthesisσ3u,v=2153+5cosusinusinv
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Curves to plot
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Expression 36: "P" left parenthesis, sigma Subscript, 1 , Baseline left parenthesis, "p" left parenthesis, "a" Subscript, 1 , Baseline , "a" Subscript, 2 , Baseline , "n" Subscript, 1 , Baseline , right parenthesis , "t" , right parenthesis , sigma Subscript, 2 , Baseline left parenthesis, "p" left parenthesis, "a" Subscript, 1 , Baseline , "a" Subscript, 2 , Baseline , "n" Subscript, 1 , Baseline , right parenthesis , "t" , right parenthesis , sigma Subscript, 3 , Baseline left parenthesis, "p" left parenthesis, "a" Subscript, 1 , Baseline , "a" Subscript, 2 , Baseline , "n" Subscript, 1 , Baseline , right parenthesis , "t" , right parenthesis , right parenthesisPσ1pa1,a2,n1,t,σ2pa1,a2,n1,t,σ3pa1,a2,n1,t
domain t Minimum: "b" Subscript, 1 , Baselineb1
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: "b" Subscript, 2 , Baselineb2
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Expression 37: "P" left parenthesis, sigma Subscript, 1 , Baseline left parenthesis, "t" , "p" left parenthesis, "b" Subscript, 1 , Baseline , "b" Subscript, 2 , Baseline , "n" Subscript, 2 , Baseline , right parenthesis , right parenthesis , sigma Subscript, 2 , Baseline left parenthesis, "t" , "p" left parenthesis, "b" Subscript, 1 , Baseline , "b" Subscript, 2 , Baseline , "n" Subscript, 2 , Baseline , right parenthesis , right parenthesis , sigma Subscript, 3 , Baseline left parenthesis, "t" , "p" left parenthesis, "b" Subscript, 1 , Baseline , "b" Subscript, 2 , Baseline , "n" Subscript, 2 , Baseline , right parenthesis , right parenthesis , right parenthesisPσ1t,pb1,b2,n2,σ2t,pb1,b2,n2,σ3t,pb1,b2,n2
domain t Minimum: "a" Subscript, 1 , Baselinea1
less than or equal to "t" less than or equal to≤t≤