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Generalized variational principle of Herglotz type fornon-conservative Lagrangian systems and its Noether’s theory(PDF)

《南京理工大学学报》（自然科学版）[ISSN:1005-9830/CN:32-1397/N]

Issue:
2019年06期
Page:
765-770
Research Field:
Publishing date:

Info

Title:
Generalized variational principle of Herglotz type fornon-conservative Lagrangian systems and its Noether’s theory
Author(s):
Tian Xue1; Zhang Yi2
1.School of Sciences,Nanjing University of Science and Technology,Nanjing 210094,China; 2.School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China
Keywords:
generalized variational principle of Herglotz type;  non-conservative Lagrangian system;  Noether’s theorem;  Noether’s inverse theorem
PACS:
O316
DOI:
10.14177/j.cnki.32-1397n.2019.43.06.014
Abstract:
In order to study non-conservative dynamic systems,Noether’s theorem and inverse theorem for non-conservative Lagrangian systems are studied by using the generalized variational principle of Herglotz type. According to the generalized variational principle of Herglotz type for the non-conservative Lagrangian system and its dynamic equation,the definition and criteria of Noether symmetry of Herglotz type are given,and the Killing equations of Herglotz type are also derived. Noether’s theorem of Herglotz type and its inverse theorem are obtained,which reveal the inner relation between the Noether symmetry and conserved quantity of the system. Taking the Emden equation and a two-freedom system as examples,the results show the Noether symmetry of Herglotz type can be used to study the Noether theory of conservative and non-conservative problems systematically.

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Last Update: 2019-12-31