The exact solution to the general relativistic differential equation describing planetary orbits

DOI10.1007/s40819-021-01019-0zbMath1499.70016OpenAlexW3158375654WikidataQ115372172 ScholiaQ115372172MaRDI QIDQ2114712

Kim Johannessen

Publication date: 15 March 2022

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40819-021-01019-0

zbMATH Keywords

Jacobi elliptic functionsMercuryperihelion precessionperiod of revolution

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics (70H40) Orbital mechanics (70M20) Equations of motion in general relativity and gravitational theory (83C10) Elliptic functions and integrals (33E05)

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Elliptic functions and applications
• Oscillators with symmetric and asymmetric quadratic nonlinearity
• The analyticity of Jacobian functions with respect to the parameter k
• A primer on elliptic functions with applications in classical mechanics
• Chaotic phenomena triggering the escape from a potential well
• Compact calculation of the perihelion precession of Mercury in general relativity, the cosmological constant and Jacobi's inversion problem
• The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations

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