Transactions of Nanjing University of Aeronautics & Astronautics
Fractional Birkhoffian Dynamics Based on Quasi-fractional Dynamics Models and Its Lie Symmetry
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Abstract:
In order to investigate the dynamic behavior of non-conservative systems， the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied. The quasi-fractional dynamics model here refers to the variational problem based on the definition of Riemann-Liouville fractional integral（RLFI）， the variational problem based on the definition of extended exponentially fractional integral（EEFI）， and the variational problem based on the definition of fractional integral extended by periodic laws（FIEPL）. First， the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established， and the corresponding Birkhoff’s equations and the determining equations of Lie symmetry are obtained. Second， for fractional Birkhoffian systems based on quasi-fractional models， the conditions and forms of conserved quantities are given， and Lie symmetry theorems are proved. The Pfaff-Birkhoff principles， Birkhoff’s equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article. Finally， some examples are given.
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Project Supported:
This work was supported by the National Natural Science Foundation of China （Nos. 11972241， 11572212 and 11272227） and the Natural Science Foundation of Jiangsu Province （No. BK20191454）.
Clc Number:
O316
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