[1] Zhang Yi,. A new method for integration of a Birkhoffian system [J]. Journal of Southeast University (English Edition), 2011, 27 (2): 188-191. [doi:10.3969/j.issn.1003-7985.2011.02.015]

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A new method for integration of a Birkhoffian system()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

27

Issue:

2011 2

Page:

188-191

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2011-06-30

Info

Title:

A new method for integration of a Birkhoffian system

Author(s):

Zhang Yi

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Keywords:

Birkhoffian system;  integration method;  basic partial differential equation

PACS:

O316

DOI:

10.3969/j.issn.1003-7985.2011.02.015

Abstract:

The idea of the gradient method for integrating the dynamical equations of a nonconservative system presented by Vujanovic’ is transplanted to a Birkhoffian system, which is a new method for the integration of Birkhoff’s equations. First, the differential equations of motion of the Birkhoffian system are written out. Secondly, 2n Birkhoff’s variables are divided into two parts, and assume that a part of the variables is the functions of the remaining part of the variables and time. Thereby, the basic quasi-linear partial differential equations are established. If a complete solution of the basic partial differential equations is sought out, the solution of the problem is given by a set of algebraic equations. Since one can choose n arbitrary Birkhoff’s variables as the functions of n remains of variables and time in a specific problem, the method has flexibility. The major difficulty of this method lies in finding a complete solution of the basic partial differential equation. Once one finds the complete solution, the motion of the systems can be obtained without doing further integration. Finally, two examples are given to illustrate the application of the results.

References:

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Memo

Memo:

Biography: Zhang Yi(1964—), male, doctor, professor, weidiezh@pub.sz.jsinfo.net.
Foundation item: The National Natural Science Foundation of China(No.10972151).
Citation: Zhang Yi. A new method for integration of a Birkhoffian system[J].Journal of Southeast University(English Edition), 2011, 27(2):188-191.[doi:10.3969/j.issn.1003-7985.2011.02.015]

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