02-15-2020, 10:01 AM

Jacobian Elliptic Functions are a set of twelve functions denoted by XY(U, K) where X and Y stands of letters c, s, n, and d. Today's blog post will focus on three of the common Jacobi Elliptic Functions:

Sine Amplitude: sn(u,k)

Cosine Amplitude: cn(u,k)

Delta Amplitude: dn(u,k)

Where u is a real number and k is a parameter between -1 and 1 inclusive

To determine any of the Jacobian Elliptic Functions, the integral has to be solved for X:

U = ∫( 1/√(1 - K^2 * sin^2(T)) dT from T = 0 to T = X)

Solving for X will represent the function am(U,K).

Then:

sn(U,K) = sin(X)

cn(U,K) = cos(X)

dn(U,K) = √(1 - K^2 * sin^2(X))

Radian angles are used.

Download: https://drive.google.com/open?id=1qQ253r...Ie2Bkgfyl_

In a different approach, I have created a custom app, which is based on the Solver App named Jacobi Elliptic Functions, which you can download on the link above.

Symb View: The four equations that are used for this app. Leave all four checked.

Num View: This is where you enter U and K. Leave these boxes unchecked. Press or touch (Solve) to get the other values am (X), sn (S), cn (C), and dn (D).

Blog post: https://edspi31415.blogspot.com/2020/02/...acobi.html

Sine Amplitude: sn(u,k)

Cosine Amplitude: cn(u,k)

Delta Amplitude: dn(u,k)

Where u is a real number and k is a parameter between -1 and 1 inclusive

To determine any of the Jacobian Elliptic Functions, the integral has to be solved for X:

U = ∫( 1/√(1 - K^2 * sin^2(T)) dT from T = 0 to T = X)

Solving for X will represent the function am(U,K).

Then:

sn(U,K) = sin(X)

cn(U,K) = cos(X)

dn(U,K) = √(1 - K^2 * sin^2(X))

Radian angles are used.

Download: https://drive.google.com/open?id=1qQ253r...Ie2Bkgfyl_

In a different approach, I have created a custom app, which is based on the Solver App named Jacobi Elliptic Functions, which you can download on the link above.

Symb View: The four equations that are used for this app. Leave all four checked.

Num View: This is where you enter U and K. Leave these boxes unchecked. Press or touch (Solve) to get the other values am (X), sn (S), cn (C), and dn (D).

Blog post: https://edspi31415.blogspot.com/2020/02/...acobi.html