TL;DR
This paper introduces the formalism and geometric framework for analyzing Hamiltonian dynamical systems with symmetry, focusing on collective motion phenomena.
Contribution
It provides a foundational geometric approach to understanding symmetry and collective motion in Hamiltonian systems, which is a novel perspective.
Findings
Develops a formalism for symmetric Hamiltonian systems
Describes geometric structures underlying collective motion
Lays groundwork for future analytical and computational methods
Abstract
This work presents the basic elements of the formalism involved in the treatment of Hamiltonian dynamical systems with symmetry and the geometrical description of collective motion.
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Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry · Slime Mold and Myxomycetes Research · Dynamics and Control of Mechanical Systems