Numerical Methods in Poisson Geometry and their Application to Mechanics

2023/03/28 by Oscar Cosserat, Cosserat, Oscar, Camille Laurent-Gengoux +3 · 2 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods for differential equations #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2303.15883

openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are compared to traditional methods.

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• Geometric theory of generalised continua using moving frames

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