how can i solve this?
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I am trying to solve this really simple code problems, but I wan not able:
Omega=zeros(1,800);
Y=cos(km2rad(20));
for n=1:800
Omega(n)=(1/2)*[(legendreP(n-1,Y))-(legendreP(n+1,Y))];
end
Omegazero=(1/2)*(1-Y);
OmegaT=[Omegazero Omega];
********************************************************************
The real formulation is:
Omega(n)=1/2[Pn-1(Y)-Pn+1(Y)],
OmegaZero=1/2(1-Y)
Y=cos(20km) that should be in radian.
I know the answer but I can not reach to real answer. I got something really different.
Thanks
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Walter Roberson
2015-11-29
编辑：Walter Roberson
2015-11-29
I could see how
Bn=2n-1/n+1*Bn-1*cos(psi)-(n-2/n+1)*Bn-2
could translate to
B(n) = (2*n-1)/(n+1) * B(n-1) * cos(psi) - (n-2)/(n+1)*B(n-2);
but where are your "3" coming from in your line
B(n)=((((2*n)-3)/(n))*B(n-1)*cos(psi))-(((n-3)/(n))*B(n-2));
?
7 个评论
Mahdiye
2015-11-29
Walter Roberson
2015-11-29
I have no idea what it means to express km in radians.
LP(1) = legendreP(1,Y);
LP(2) = legendreP(2,Y);
for n = 1:800
LP(n+2) = legendreP(n+2,Y);
Omega(n) =(1/2)*(LP(n)-LP(n+2));
end
You might need to define
legendreP = @(n,x) double( feval(symengine, 'legendreP', n, x) );
Mahdiye
2015-11-29
编辑：Walter Roberson
2015-11-29
Walter Roberson
2015-11-29
Yes you are right that LP(n+2) = legendreP(n+1,Y)
You have defined the size of the sphere (20 km) but you have not defined the angle to be subtended. km2rad(Distance) by default means
fraction = Distance / (2 * pi * radius_of_Earth_in_km)
radians = fraction * (2 * pi)
which works out as
radians = Distance / radius_of_Earth_in_km
If you want to use a sphere with a radius different than the radius of the Earth then you would need to use km2rad with two parameters. km2rad(Distance, radius_in_km). For a sphere of radius 20 km you would use km2rad(Distance, 20) which would come out as
radians = Distance / 20
But notice that you need to define the Distance.
Radians is 2 * Pi * fraction around the circle that you have traveled. And that information about how far around the circle you have traveled is missing at this time: you have only defined how big the circle is.
Walter Roberson
2015-11-30
That calculation looks okay.
legendreP is part of the symbolic toolbox, so it is only invoked if at least one of the arguments to it is symbolic, but you are wanting to invoke it with arguments that are completely numeric. legendreP(numeric,numeric) would not be found -- without a symbolic parameter MATLAB does not have reason to look in the symbolic toolbox for a match.
legendreP = @(n,x) double( feval(symengine, 'legendreP', n, x) );
locally defines legendreP as an anonymous function with two arguments that invokes the symbolic engine (MuPAD) directly and tells the symbolic engine to execute the MuPAD function legendreP with the two given arguments. With this direct call, MATLAB will be able to find the correct function and execute it, returning a symbolic number as a solution; double() then converts the symbolic number to a floating point number that MATLAB can use.
Walter Roberson
2015-12-2
编辑：Walter Roberson
2015-12-2
Mahdiye comments "Wonderful answer"
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