# Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

## Abstract

A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of second-class constraints in the formalism which are handled using the procedure of Rothe and Scholtz recently reported. The current method is applied to the non-relativistic two-dimensional isotropic harmonic oscillator employing the various symplectic structures for this dynamical system recently reported.

- Authors:

- Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del I.P.N., Av. I.P.N. No. 2508, 07000 Ciudad de Mexico (Mexico). E-mail: amerino@fis.cinvestav.mx
- Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del I.P.N., Av. I.P.N. No. 2508, 07000 Ciudad de Mexico (Mexico). E-mail: merced@fis.cinvestav.mx

- Publication Date:

- OSTI Identifier:
- 20766984

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 321; Journal Issue: 2; Other Information: DOI: 10.1016/j.aop.2005.08.008; PII: S0003-4916(05)00140-5; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTON-JACOBI EQUATIONS; HAMILTONIANS; HARMONIC OSCILLATORS; RELATIVISTIC RANGE; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Martinez-Merino, Aldo A., and Montesinos, Merced.
```*Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures*. United States: N. p., 2006.
Web. doi:10.1016/j.aop.2005.08.008.

```
Martinez-Merino, Aldo A., & Montesinos, Merced.
```*Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures*. United States. doi:10.1016/j.aop.2005.08.008.

```
Martinez-Merino, Aldo A., and Montesinos, Merced. Wed .
"Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures". United States.
doi:10.1016/j.aop.2005.08.008.
```

```
@article{osti_20766984,
```

title = {Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures},

author = {Martinez-Merino, Aldo A. and Montesinos, Merced},

abstractNote = {A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of second-class constraints in the formalism which are handled using the procedure of Rothe and Scholtz recently reported. The current method is applied to the non-relativistic two-dimensional isotropic harmonic oscillator employing the various symplectic structures for this dynamical system recently reported.},

doi = {10.1016/j.aop.2005.08.008},

journal = {Annals of Physics (New York)},

number = 2,

volume = 321,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}

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