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Blow up of mechanical systems with a homogeneous energy.

Ernesto A. Lacomba, John Bryant, Luis Alberto Ibort (1991)

Publicacions Matemàtiques

By using the ideas introduced by McGehee in the study of the singularities in some problems of Celestial Mechanics, we study the singularities at the origin and at the infinity for some classical mechanical systems with homogeneous kinetic and potential energy functions. For these systems the origin and the infinity of the configuration coordinates is usually a singularity or a nullity of the Hamiltonian function and the verctor field. This work generalizes a previous one by the first and the third...

Non-decomposable Nambu brackets

Klaus Bering (2015)

Archivum Mathematicum

It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.

Non-holonomic mechanical systems in jet bundles.

Manuel de León, David Martín de Diego (1996)

Extracta Mathematicae

In this paper we present a geometrical formulation for Lagrangian systems subjected to non-holonomic constraints in terms of jet bundles. Cosymplectic geometry and almost product structures are used to obtained the constrained dynamics without using Lagrange multipliers method.

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