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10Â¥: Originally posted by cooooldog at 2016-03-22 08:59:16
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sweety   hsd3521...

ClearAll["Global`*"];
R = 4878/100;
z1 = 6;
r = R/z1;
z2 = z1 - 1;
e = 705/100;
f = r/e;
re = 126/10;
¦È = ArcTan[Sin[z1 ¦Ó]/(f + Cos[z1 ¦Ó])] - ¦Ó;
¦Õ = ArcSin[f Sin[¦È + ¦Ó]] - ¦È;
¦× = z1/(z1 - 1) ¦Õ;

(* Á½¸ö²ÎÊý·½³Ì *)
curve01 = {(R - r) Sin[¦Ó] + e Sin[z2 ¦Ó] -  re Sin[¦È], (R - r) Cos[¦Ó] - e Cos[z2 ¦Ó] +  re Cos[¦È]} // Simplify;

(*¶¨×Ó*)
ParametricPlot[curve01,{¦Ó,0,2 ¦Ð},Exclusions\[Rule]None,MaxRecursion\[Rule]15,PlotPoints->
500,PlotStyle->Red]


(*ת×Ó*)
curve02 = {curve01[[1]] Cos[¦Õ - ¦×] -  curve01[[2]] Sin[¦Õ - ¦×] - e Sin[¦×],
    curve01[[1]] Sin[¦Õ - ¦×] +   curve01[[2]] Cos[¦Õ - ¦×] - e Cos[¦×]} //Simplify;

base=ParametricPlot[curve02,{¦Ó,0,2 ¦Ð},Exclusions->None,MaxRecursion->15,PlotPoints->500,PlotStyle->Blue]; Show[base]

¦Óp = (y - x) /.FindRoot[(curve02 /. ¦Ó -> x) == (curve02 /. ¦Ó -> y), {x, Pi/20}, {y, 2 Pi}];

arc = Table[curve02, {¦Ó, 0, ¦Óp/10, .00001}];

Show[base,Graphics[{{Red,Line[{curve02 /. ¦Ó -> 0, {0, 0},curve02 /. ¦Ó -> ¦Óp/10}], Line@arc}}]]

¦Óp = 5 Pi/3;
5 (NIntegrate[-First[curve02] D[Last@curve02, ¦Ó] +  Last[curve02] D[First@curve02, ¦Ó], {¦Ó, 0, ¦Óp/10}, Method -> "LocalAdaptive", MaxRecursion -> 100]) // NumberForm[#, 15] &

curveArea[r_]:=Module[{z1,z2,e,f,re,R,¦È,¦Õ,¦×,¦Ó,curve01,curve02},
z1=6;
R=r z1;
z2=z1-1;
e=705/100;
f=r/e;
re=126/10;
¦È=ArcTan[Sin[z1 ¦Ó]/(f+Cos[z1 ¦Ó])]-¦Ó;
¦Õ=ArcSin[f Sin[¦È+¦Ó]]-¦È;
¦×=z1/(z1-1) ¦Õ;
curve01={(R-r) Sin[¦Ó]+e Sin[z2 ¦Ó]-re Sin[¦È],(R-r) Cos[¦Ó]-e Cos[z2 ¦Ó]+re Cos[¦È]};curve02={curve01[[1]] Cos[¦Õ-¦×]-curve01[[2]] Sin[¦Õ-¦×]-e Sin[¦×],curve01[[1]] Sin[¦Õ-¦×]+curve01[[2]] Cos[¦Õ-¦×]-e Cos[¦×]};
(5 (NIntegrate[-First[curve02] D[Last@curve02,¦Ó]+Last[curve02] D[First@curve02,¦Ó],{¦Ó,0,¦Óp/20,¦Óp/10},MaxRecursion->100,Method->"LocalAdaptive"]))
]

FindRoot[curveArea[x] == 6557.19, {x, 7.5}, Evaluated -> False,Method -> {"Newton", "StepControl" -> "TrustRegion"}] // AbsoluteTiming

r=8.1294128480878

11Â¥: Originally posted by Mr__Right at 2016-03-22 20:57:03
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ClearAll;
R = 4878/100;
z1 = 6;
r = R/z1;
z2 = z1 - 1;
e = 705/100;
...

10Â¥: Originally posted by cooooldog at 2016-03-22 08:59:16
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sweety   hsd3521...

11Â¥: Originally posted by Mr__Right at 2016-03-22 20:57:03
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¹¤¾ß£ºÓÃMathematica ½â¾ö¡£Çó½âÕâÀàÎÊÌ⣬MathematicaÊ×ÇüÒ»Ö¸¡£

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ClearAll;
R = 4878/100;
z1 = 6;
r = R/z1;
z2 = z1 - 1;
e = 705/100;
...

12¥: Originally posted by ѾͷѾͷ2014 at 2016-05-17 10:49:39
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