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

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Gebreel Mohammed Khur Baba Gebreel
Gebreel Mohammed Khur Baba Gebreel
2
Mohammed Ali Bashir
Mohammed Ali Bashir

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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.

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No external funding was declared for this work.

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The authors declare no conflict of interest.

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Gebreel Mohammed Khur Baba Gebreel. 2020. \u201cOn the Standard Cliffordian Hamiltonian Formulation of Symplectic Mechanics Using Frame and Co-Frame fields\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F1): .

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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 37K05
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v1.2

Issue date

February 18, 2020

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English

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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.

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

Gebreel Mohammed Khur Baba Gebreel
Gebreel Mohammed Khur Baba Gebreel
Mohammed Ali Bashir
Mohammed Ali Bashir

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