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Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.

Ernesto A. Lacomba, J. Guadalupe Reyes (1998)

Publicacions Matemàtiques

We extend here results for escapes in any given direction of the configuration space of a mechanical system with a non singular bounded at infinity homogeneus potential of degree -1, when the energy is positive. We use geometrical methods for analyzing the parallel and asymptotic escapes of this type of systems. By using Riemannian geometry methods we prove under suitable conditions on the potential that all the orbits escaping in a given direction are asymptotically parallel among themselves. We...

Non-cooperative game approach to multi-robot planning

Adam Gałuszka, Andrzej Świerniak (2005)

International Journal of Applied Mathematics and Computer Science

A multi-robot environment with a STRIPS representation is considered. Under some assumptions such problems can be modelled as a STRIPS language (for instance, a Block World environment) with one initial state and a disjunction of goal states. If the STRIPS planning problem is invertible, then it is possible to apply the machinery for planning in the presence of incomplete information to solve the inverted problem and then to find a solution to the original problem. In the paper a planning algorithm...

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.

Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory

Andrzej J. Maciejewski (2002)

Banach Center Publications

The aim of this paper is to present two examples of non academic Hamiltonian systems for which the Morales-Ramis theory can be applied effectively. First, we investigate the Gross-Neveu system with n degrees of freedom. Till now it has been proved that this system is not integrable for n = 3. We give a simple proof that it is not completely integrable for an arbitrary n ≥ 3. Our second example is a natural generalisation of the Jacobi problem of a material point moving on an ellipsoid. We formulate...

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