Poincaré-Cartan integral invariants of Birkhoffian systems

Yong Xin Guo; Mei Shang; Shao Kai Luo

doi:10.1007/bf02439379

Poincaré-Cartan integral invariants of Birkhoffian systems

Yong Xin Guo^*, Mei Shang, Shao Kai Luo

^*Corresponding author for this work

School of Aerospace Engineering

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

6 Citations (Scopus)

Abstract

Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan's type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as on illustrative example and integral invariant of Poincaré's type is found.

Original language	English
Pages (from-to)	68-72
Number of pages	5
Journal	Applied Mathematics and Mechanics (English Edition)
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/bf02439379
Publication status	Published - Jan 2003

Keywords

Birkhoffian systems
Poincaré-Cartan integral invariants
Self-adjointness
Symplectic structure

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10.1007/bf02439379

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title = "Poincar{\'e}-Cartan integral invariants of Birkhoffian systems",

abstract = "Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincar{\'e}-Cartan's type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as on illustrative example and integral invariant of Poincar{\'e}'s type is found.",

keywords = "Birkhoffian systems, Poincar{\'e}-Cartan integral invariants, Self-adjointness, Symplectic structure",

author = "Guo, \{Yong Xin\} and Mei Shang and Luo, \{Shao Kai\}",

year = "2003",

month = jan,

doi = "10.1007/bf02439379",

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AU - Guo, Yong Xin

AU - Shang, Mei

AU - Luo, Shao Kai

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N2 - Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan's type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as on illustrative example and integral invariant of Poincaré's type is found.

AB - Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan's type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as on illustrative example and integral invariant of Poincaré's type is found.

KW - Birkhoffian systems

KW - Poincaré-Cartan integral invariants

KW - Self-adjointness

KW - Symplectic structure

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DO - 10.1007/bf02439379

M3 - Article

AN - SCOPUS:0038545524

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JO - Applied Mathematics and Mechanics (English Edition)

JF - Applied Mathematics and Mechanics (English Edition)

IS - 1

ER -

Poincaré-Cartan integral invariants of Birkhoffian systems

Abstract

Keywords

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