Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications requi...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2013 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2013
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149209 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass / Sara Cruz y Cruz, Oscar Rosas-Ortiz // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 46 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862656018440257536 |
|---|---|
| author | Sara Cruz y Cruz Rosas-Ortiz, Oscar |
| author_facet | Sara Cruz y Cruz Rosas-Ortiz, Oscar |
| citation_txt | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass / Sara Cruz y Cruz, Oscar Rosas-Ortiz // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 46 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications required in the Euler-Lagrange and Hamilton's equations to reproduce the appropriate Newton's dynamical law. Since the Hamiltonian is not time invariant, we get a constant of motion suited to write the dynamical equations in the form of the Hamilton's ones. The time-dependent first integrals of motion are then obtained from the factorization of such a constant. A canonical transformation is found to map the variable mass equations to those of a constant mass. As particular cases, we recover some recent results for which the dependence of the mass on the position was already unnoticed, and find new solvable potentials of the Pöschl-Teller form which seem to be new. The latter are associated to either the su(1,1) or the su(2) Lie algebras depending on the sign of the Hamiltonian.
|
| first_indexed | 2025-12-02T04:27:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149209 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T04:27:21Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sara Cruz y Cruz Rosas-Ortiz, Oscar 2019-02-19T18:43:27Z 2019-02-19T18:43:27Z 2013 Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass / Sara Cruz y Cruz, Oscar Rosas-Ortiz // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 46 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q99; 37J99; 70H03; 70H05 DOI: http://dx.doi.org/10.3842/SIGMA.2013.004 https://nasplib.isofts.kiev.ua/handle/123456789/149209 We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications required in the Euler-Lagrange and Hamilton's equations to reproduce the appropriate Newton's dynamical law. Since the Hamiltonian is not time invariant, we get a constant of motion suited to write the dynamical equations in the form of the Hamilton's ones. The time-dependent first integrals of motion are then obtained from the factorization of such a constant. A canonical transformation is found to map the variable mass equations to those of a constant mass. As particular cases, we recover some recent results for which the dependence of the mass on the position was already unnoticed, and find new solvable potentials of the Pöschl-Teller form which seem to be new. The latter are associated to either the su(1,1) or the su(2) Lie algebras depending on the sign of the Hamiltonian. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html.
 The authors thank the anonymous referees for their comments to improve the presentation and motivation of the paper. The financial support of CONACyT-Mexico (project 152574), MICINN-Spain (project MTM2009-10751), IPN grant COFAA and projects SIP20120451, SIPSNIC-2011/04, is acknowledged. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass Article published earlier |
| spellingShingle | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass Sara Cruz y Cruz Rosas-Ortiz, Oscar |
| title | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass |
| title_full | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass |
| title_fullStr | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass |
| title_full_unstemmed | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass |
| title_short | Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass |
| title_sort | dynamical equations, invariants and spectrum generating algebras of mechanical systems with position-dependent mass |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149209 |
| work_keys_str_mv | AT saracruzycruz dynamicalequationsinvariantsandspectrumgeneratingalgebrasofmechanicalsystemswithpositiondependentmass AT rosasortizoscar dynamicalequationsinvariantsandspectrumgeneratingalgebrasofmechanicalsystemswithpositiondependentmass |