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Title:
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Structural aspects of Hamilton–Jacobi theory
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Author:
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Cariñena Marzo, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez Fernandez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions |
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Abstract:
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The final publication is available at Springer via http://dx.doi.org/10.1142/S0219887816500171 |
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Abstract:
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In our previous papers [11, 13] we showed that the Hamilton–Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton–Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (‘slicing vector fields’) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton– Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
-Hamiltonian systems
-Mechanics
-Hamilton-Jacobi equation
-slicing vector field
-complete solution
-constant of the motion
-Hamilton, Sistemes de
-Mecànica
-Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
-Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods |
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Rights:
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Document type:
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Article - Submitted version
Article |
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