The interplay between Dirac systems, Morse families and Interconnection

2017/02/28 by María Barbero-Liñán, Barbero-Liñán, M., Hernán Cendra +5
Biochemistry, Genetics and Molecular Biology · Engineering · #ATP Synthase and ATPases Research #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1702.08596

openalex publication_date 2017/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrained variational calculus, optimal control, Lagrangian mechanics, etc., from both the Lagrangian and the Hamiltonian viewpoint. Besides, we introduce a geometric construction of Port-Dirac systems and use it to describe the interconnection of Dirac systems. Special emphasis on theoretical and applied examples is given throughout the paper to show the applicability of the proposed framework.

Citations

• Symplectic manifolds and their lagrangian submanifolds

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