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Conservation laws for Birkhoffian systems of Herglotz type |
| Yi Zhang(张毅)1, Xue Tian(田雪)2 |
1 College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China;
2 College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China |
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Abstract Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied. We propose a new differential variational principle, called the Pfaff-Birkhoff-d'Alembert principle of Herglotz type. Birkhoff's equations for both the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are obtained. According to the relationship between the isochronal variation and the nonisochronal variation, the conditions of the invariance for the Pfaff-Birkhoff-d'Alembert principle of Herglotz type are given. Then, the conserved quantities for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are deduced. Furthermore, the inverse theorems of the conservation theorems are also established.
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Received: 20 March 2018
Revised: 29 May 2018
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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11.30.-j
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(Symmetry and conservation laws)
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45.10.Db
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(Variational and optimization methods)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11572212 and 11272227), the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province, China (Grant No. KYZZ16_0479), and the Innovation Program for Postgraduate of Suzhou University of Science and Technology, China (Grant No. SKCX16_058). |
Corresponding Authors:
Yi Zhang
E-mail: zhy@mail.usts.edu.cn
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Cite this article:
Yi Zhang(张毅), Xue Tian(田雪) Conservation laws for Birkhoffian systems of Herglotz type 2018 Chin. Phys. B 27 090502
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