Two families of nonstandard Poisson structures for Newton equations

DOI10.1063/1.532571zbMath0940.70010OpenAlexW1991248733MaRDI QIDQ4701484

Krzysztof Marciniak, Stefan Rauch-Wojciechowski

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532571

zbMATH Keywords

Newton equationsseparable systemsbi-Hamiltonian formulationquasi-Lagrangian systemstwo-dimensional Poisson structures

Mathematics Subject Classification ID

Hamilton's equations (70H05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

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Cites Work

• What is a classical r-matrix?
• Completely integrable systems, Euclidean Lie algebras, and curves
• Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
• Separation of variables on n-dimensional Riemannian manifolds. I. The n-sphere S n and Euclidean n-space R n
• When is a Hamiltonian system separable?

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