On the Construction of Poincaré–Lindstedt Solutions: The Nonlinear Oscillator Equation
Peter J. Melvin
Source abstract
The equation of motion in a potential energy well is formally integrated by a combined power and Fourier series. A new notation is used to reduce the integration problem to the algebraic problem of the solution of two recursion relations in a finite form. Two general algorithms are obtained from the recursion relations for motions in asymmetrical and symmetrical, parabolic wells. A third algorithm is presented for the periodic solutions of a form of the Emden–Fowler equation. The computer versions of the algorithms for parabolic wells are checked against independent analytical solutions of the equation for time dependent radial motion in the Newtonian two-body problem and the equation of Blasius. The limitations of the solutions to small to moderate amplitudes are found by the analytical-computer solution of the radial part of the orbital and scattering notions in a Lennard–Jones six-twelve potential.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.