On the Standard Cliffordian Hamiltonian Formulation of Symplectic Mechanics Using Frame and Co-Frame fields

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On the Standard Cliffordian Hamiltonian Formulation of Symplectic Mechanics  Using Frame and Co-Frame fields

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Abstract

In the standard Cliffordian Hamiltonian mechanics we use canonical local basis {𝐽𝐽 1 * , 𝐽𝐽 2 * , 𝐽𝐽 3 * }. In this paper using the frame fields 𝑖𝑖 𝑋𝑋 = 𝑋𝑋 𝑎𝑎𝑎𝑎 +𝑖𝑖 𝜕𝜕 𝜕𝜕𝑥𝑥 𝑎𝑎𝑎𝑎 +𝑖𝑖 , 𝑎𝑎 = 0,1,2, … ,7 instead of the Hamiltonian vector field in the Cliffordian Hamiltonian formulation we verified the generalized form of Hamiltonian equation which is in conformity with the results that have been obtained previously.

References

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  4. Gebreel Mohammed,Khur Baba Gebreel,M Bashir (2017). On a new dynamics on 𝐾𝐾𝑑𝑑̈ℎ𝑑𝑑𝑑𝑑𝑙𝑙 manifold using local canonical basis.
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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Gebreel Mohammed Khur Baba Gebreel, Mohammed Ali Bashir, <[email protected]. 2020. "On the Standard Cliffordian Hamiltonian Formulation of Symplectic Mechanics Using Frame and Co-Frame fields". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F1).

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
GJSFR-F Classification MSC 2010: 37K05
Version of record

v1.2

Issue date
February 18, 2020

Language
English
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On the Standard Cliffordian Hamiltonian Formulation of Symplectic Mechanics Using Frame and Co-Frame fields

Gebreel Gebreel
Gebreel Gebreel <p>West Kordufan University</p>
Mohammed Bashir
Mohammed Bashir