Symmetric Solutions to Nonlinear Vectorial 2nd Order ODE's

2021/12/21 by Ali Abdulhussein, Abdulhussein, Ali, Harry Gingold +1
Engineering · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Nonlinear Waves and Solitons #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2112.11528

openalex publication_date 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proven that second-order vectorial nonlinear differential systems y''=f(y) , possess a continuum of symmetric solutions. They are shown to possess a continuum of even solutions. If f(y) is an odd function of y , then y''=f(y) is shown also to possess a continuum of odd solutions. The results apply to a significant family of second-order vectorial nonlinear differential systems that are not dissipative. This family of differential equations includes the celebrated N-body problem of celestial mechanics and other central force problems.

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