Theory of Generalized Canonical Transformations for Birkhoff Systems
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-05-26
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Transformation is an important means to study problems in analytical mechanics.
It is often difficult to solve dynamic equations, and the use of variable transformation can make the equations easier to solve.
The theory of canonical transformations plays an important role in solving Hamilton’s canonical equations.
Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics.
This paper attempts to extend the canonical transformation theory of Hamilton systems to Birkhoff systems and establish the generalized canonical transformation of Birkhoff systems.
First, the definition and criterion of the generalized canonical transformation for the Birkhoff system are established.
Secondly, based on the criterion equation and considering the generating functions of different forms, six generalized canonical transformation formulas are derived.
As special cases, the canonical transformation formulas of classical Hamilton’s equations are given.
At the end of the paper, two examples are given to illustrate the application of the results.
American Psychological Association (APA)
Zhang, Yi. 2020. Theory of Generalized Canonical Transformations for Birkhoff Systems. Advances in Mathematical Physics،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1127576
Modern Language Association (MLA)
Zhang, Yi. Theory of Generalized Canonical Transformations for Birkhoff Systems. Advances in Mathematical Physics No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1127576
American Medical Association (AMA)
Zhang, Yi. Theory of Generalized Canonical Transformations for Birkhoff Systems. Advances in Mathematical Physics. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1127576
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1127576