Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems

M. Avendaño-Camacho; J. A. Vallejo; Yu Vorobiev

doi:10.1063/1.4817863

Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems

M. Avendaño-Camacho^*, J. A. Vallejo, Yu Vorobiev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with S¹-symmetry. Explicit global formulas for approximate second-order first integrals are derived. As examples, we analyze the case quadratic in the fast variables (in particular, the elastic pendulum), and the charged particle in a slowly-varying magnetic field.

Original language	English
Article number	082704
Journal	Journal of Mathematical Physics
Volume	54
Issue number	8
DOIs	https://doi.org/10.1063/1.4817863
State	Published - 5 Aug 2013

Bibliographical note

Funding Information:
Partially supported by the Mexican Consejo Nacional de Ciencia y Tecnología (CONACyT), Project CD-2012 179115 (JAV).

Access to Document

10.1063/1.4817863

Cite this

@article{0712b4618c6240a1b484b26b9efd8201,

title = "Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems",

abstract = "We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with S1-symmetry. Explicit global formulas for approximate second-order first integrals are derived. As examples, we analyze the case quadratic in the fast variables (in particular, the elastic pendulum), and the charged particle in a slowly-varying magnetic field.",

author = "M. Avenda{\~n}o-Camacho and Vallejo, {J. A.} and Yu Vorobiev",

note = "Funding Information: Partially supported by the Mexican Consejo Nacional de Ciencia y Tecnolog{\'i}a (CONACyT), Project CD-2012 179115 (JAV).",

year = "2013",

month = aug,

day = "5",

doi = "10.1063/1.4817863",

language = "Ingl{\'e}s",

volume = "54",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics",

number = "8",

}

TY - JOUR

T1 - Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems

AU - Avendaño-Camacho, M.

AU - Vallejo, J. A.

AU - Vorobiev, Yu

N1 - Funding Information: Partially supported by the Mexican Consejo Nacional de Ciencia y Tecnología (CONACyT), Project CD-2012 179115 (JAV).

PY - 2013/8/5

Y1 - 2013/8/5

N2 - We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with S1-symmetry. Explicit global formulas for approximate second-order first integrals are derived. As examples, we analyze the case quadratic in the fast variables (in particular, the elastic pendulum), and the charged particle in a slowly-varying magnetic field.

AB - We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with S1-symmetry. Explicit global formulas for approximate second-order first integrals are derived. As examples, we analyze the case quadratic in the fast variables (in particular, the elastic pendulum), and the charged particle in a slowly-varying magnetic field.

UR - http://www.scopus.com/inward/record.url?scp=84883410022&partnerID=8YFLogxK

U2 - 10.1063/1.4817863

DO - 10.1063/1.4817863

M3 - Artículo

SN - 0022-2488

VL - 54

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 8

M1 - 082704

ER -

Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this