Parameter-Adjusting Method of Constructing Birkhoffian Functions

SONG Duan; LIU Chang; GUO Yong-xin

doi:10.3879/j.issn.1000-0887.2013.09.013

Volume 34 Issue 9

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SONG Duan, LIU Chang, GUO Yong-xin. Parameter-Adjusting Method of Constructing Birkhoffian Functions[J]. Applied Mathematics and Mechanics, 2013, 34(9): 995-1002. doi: 10.3879/j.issn.1000-0887.2013.09.013

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Parameter-Adjusting Method of Constructing Birkhoffian Functions

doi: 10.3879/j.issn.1000-0887.2013.09.013

¹Department of Imaging Physics, Eastern Liaoning University, Dandong, Liaoning 118001, P.R.China;²College of Physics, Liaoning University, Shenyang 110036, P.R.China;³School of Mechanical and Electrical Engineering, Eastern Liaoning University, Dandong, Liaoning 118001, P.R.China

Funds: The National Natural Science Foundation of China（11172120;11202090;10932002）

Received Date: 2013-07-22
Rev Recd Date: 2013-09-09
Publish Date: 2013-09-15

Abstract

Abstract

The parameter-adjusting method to construct dynamical functions of Birkhoff's equations is put forward based on realizing the completeness of Birkhoff’s equations, which are under-determinate, by means of Cauchy-Kovalevski integrability theorem for partial differential equations. The two kinds of parameters in the compensatory equation were capable of adjusting to get different sets of Birkhoffian functions. The existing methods, such as Hojman’s method using 2n-first integrals for dynamical systems with symmetry, were compared with the parameter-adjusting method. Finally, The compensatory equation for the Birkhoff's equations can be simplified by means of some limitations on the two kinds of parameters, where the relation between the Birkhoffian functions and parameters become more evident.
- Birkhoff’s equations,
- Cauchy-Kovalevski theorem,
- self-adjoint differential equations,
- parameter-adjusting method

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References(15)

References

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