jacobiAM

Jacobi amplitude function

Description

example

jacobiAM(u,m) returns the Jacobi Amplitude Function of u and m. If u or m is an array, then jacobiAM acts element-wise.

Examples

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jacobiAM(2,1)
ans =
1.3018

Call jacobiAM on array inputs. jacobiAM acts element-wise when u or m is an array.

jacobiAM([2 1 -3],[1 2 3])
ans =
1.3018    0.7370    0.6155

Convert numeric input to symbolic form using sym, and find the Jacobi amplitude function. For symbolic input where u = 0 or m = 0 or 1, jacobiAM returns exact symbolic output.

jacobiAM(sym(2),sym(1))
ans =
2*atan(exp(2)) - pi/2

Show that for other values of u or m, jacobiAM returns an unevaluated function call.

jacobiAM(sym(2),sym(3))
ans =
jacobiAM(2, 3)

For symbolic variables or expressions, jacobiAM returns the unevaluated function call.

syms x y
f = jacobiAM(x,y)
f =
jacobiAM(x, y)

Substitute values for the variables by using subs, and convert values to double by using double.

f = subs(f, [x y], [3 5])
f =
jacobiAM(3, 5)
fVal = double(f)
fVal =
0.0311

Calculate f to higher precision using vpa.

fVal = vpa(f)
fVal =
0.031149815412430844987208470634926

Plot the Jacobi amplitude function using fcontour. Set u on the x-axis and m on the y-axis by using the symbolic function f with the variable order (u,m). Fill plot contours by setting Fill to on.

syms f(u,m)
f(u,m) = jacobiAM(u,m);
fcontour(f,'Fill','on')
title('Jacobi Amplitude Function')
xlabel('u')
ylabel('m') Input Arguments

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Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.

Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.

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Jacobi Amplitude Function

The Jacobi amplitude function am(u,m) is defined by am(u,m) = φ where F(φ,m) = u and F represents the incomplete elliptic integral of the first kind. F is implemented as ellipticF.