Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic

DOI10.1007/s10569-008-9177-yzbMath1223.70004OpenAlexW1985867766MaRDI QIDQ642313

Toshio Fukushima

Publication date: 26 October 2011

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-008-9177-y

zbMATH Keywords

numerical methodrotationelliptic integralsJacobian elliptic functionsextended body dynamics

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Free motion of a rigid body (70E15) Computation of special functions and constants, construction of tables (65D20) Elliptic functions and integrals (33E05)

Related Items (11)

Dynamics of a particle under the gravitational potential of a massive annulus: properties and equilibrium description ⋮ 2-D Duffing oscillator: elliptic functions from a dynamical systems point of view ⋮ Precise and fast computation of a general incomplete elliptic integral of third kind by half and double argument transformations ⋮ Computation of families of periodic orbits and bifurcations around a massive annulus ⋮ Precise and fast computation of Jacobian elliptic functions by conditional duplication ⋮ Fast computation of complete elliptic integrals and Jacobian elliptic functions ⋮ Precise computation of acceleration due to uniform ring or disk ⋮ Fast computation of a general complete elliptic integral of third kind by half and double argument transformations ⋮ Precise and fast computation of the general complete elliptic integral of the second kind ⋮ Precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations ⋮ Fast computation of incomplete elliptic integral of first kind by half argument transformation

Uses Software

• Mathematica
• algorithm 577

Cites Work

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• Dynamic discretization method for solving Kepler's equation
• Exact solution of a triaxial gyrostat with one rotor
• Computing elliptic integrals by duplication
• A fast procedure solving Gauss' form of Kepler's equation
• Numerical computation of incomplete elliptic integrals of a general form
• A method solving Kepler's equation without transcendental function evaluations
• A method solving Kepler's equation for hyperbolic case
• Fast procedure solving universal Kepler's equation
• Numerical calculation of elliptic integrals and elliptic functions.II
• Numerical calculation of elliptic integrals and elliptic functions
• An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind
• Numerical calculation of elliptic integrals and elliptic functions. III
• Algorithm 577: Algorithms for Incomplete Elliptic Integrals [S21]
• Elliptic Integrals of the First Kind

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