iloverangers

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12 years, 259 days

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These are questions asked by iloverangers

So far I have a circle with a cornu spiral joining where their curvatures are equal as below.

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

R1:=1;

u1:=evalf(sqrt(0.4));

E1:=evalf(Pi*R1*S1(u1)+R1);

D1:=evalf(Pi*R1*C1(u1));

with(plottools);

with(plots);

c1 := circle([D1, E1], R1);

display(c1);

a:=evalf(Pi*R1*u1);

Here is my working so far

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

with(plottools);

with(plots);

u0:=sqrt(0.25);

evalf(FresnelC(u0)+FresnelS(u0)*cot((3*Pi)/8));

p1:=display(plot([FresnelC(u),FresnelS(u),u=0..u0]));

p2:=display(plot(x-0.5191572775,x=0..1,y=0..1,colour=black));

display(p1,p2);

I have two graphs but can't work out how to put them together. Anyone have any idea? Below is my program

C1(u):=u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2));

S1(u):=u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi);

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

R0:=0.7;

R1:=1.5;

evalf((R0+R1)*(((Pi*C1(1))^2+(Pi*S1(1)+1)^2))^(1/2));

T:=1.8;

A:=fsolve(T=(R0+R1)*(((Pi*C1(B))^2+(Pi*S1(B)+1)^2))^(1/2),B,0..1);

a0:=evalf(Pi*R0*A);

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