Class EllipticFunctions

java.lang.Object
org.episteme.core.mathematics.analysis.special.EllipticFunctions
public class EllipticFunctions extends Object
Elliptic integrals and Jacobi elliptic functions.

Essential for pendulum motion, electromagnetic theory, and orbital mechanics.

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • EllipticFunctions

      public EllipticFunctions()

  • Method Details

    • completeK

      public static Real completeK(Real m)
      Complete elliptic integral of the first kind: K(m).

      $K(m) = \int_0^{\pi/2} \frac{d\theta}{\sqrt{1 - m\sin^2\theta}}$

      Parameters:
      m - Parameter (0 ≤ m invalid input: '<' 1)
      Returns:
      K(m)

    • completeK

      public static double completeK(double m)

    • completeE

      public static Real completeE(Real m)
      Complete elliptic integral of the second kind: E(m).

      $E(m) = \int_0^{\pi/2} \sqrt{1 - m\sin^2\theta} d\theta$

      Parameters:
      m - Parameter (0 ≤ m ≤ 1)
      Returns:
      E(m)

    • completeE

      public static double completeE(double m)

    • incompleteF

      public static double incompleteF(double phi, double m)
      Incomplete elliptic integral of the first kind: F(φ, m).

      $F(\phi, m) = \int_0^{\phi} \frac{d\theta}{\sqrt{1 - m\sin^2\theta}}$

      Parameters:
      phi - Amplitude angle (radians)
      m - Parameter (0 ≤ m invalid input: '<' 1)
      Returns:
      F(φ, m)

    • jacobi

      public static double[] jacobi(double u, double m)
      Jacobi elliptic functions sn, cn, dn.

      Returns [sn(u,m), cn(u,m), dn(u,m)].

      Parameters:
      u - Argument
      m - Parameter (0 ≤ m ≤ 1)
      Returns:
      Array [sn, cn, dn]

    • sn

      public static Real sn(Real u, Real m)

    • cn

      public static Real cn(Real u, Real m)

    • dn

      public static Real dn(Real u, Real m)