Year: 2025
Type: article
Abstract: This work introduces a methodology for generating linear operators that approximately represent nonlinear systems of perturbed ordinary differential equations. This is done through the application of classical perturbation theory via the Lindstedt–Poincaré expansion, followed by an extension of the space of configuration that guarantees the linear representation of the expanded system of differential equations. To ensure that such a linear representation exists, this paper uses polynomial basis functions. Pseudocode describing the implementation of the proposed method is listed. The method is applied to the Duffing oscillator as well as to the [Formula: see text] problem, with and without atmospheric drag, both analyzed using an osculating formulation. Additionally, conditions on the osculating Keplerian elements that produce low-eccentricity frozen orbits are presented, and a modification of the Lindstedt–Poincaré method is proposed to enable the generation of linear operators that dynamically adapt to changes in the frequency of the motion. Finally, the proposed method is compared with alternatives in the literature.
DOI: 10.2514/1.g008683
Authors: Miguel Avillez, David Arnas
Institution: Purdue University West Lafayette
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409214984