scholarly journals The conserved quantity of Hojman for mechanicalsystems with variable mass in phase space

2004 ◽  
Vol 53 (12) ◽  
pp. 4041
Author(s):  
Fang Jian－Hui ◽  
Zhang Peng－Yu
Keyword(s):  
Phase Space ◽  
Variable Mass ◽  
Conserved Quantity

A Unified Symmetry of Mechanical Systems with Variable Mass in Phase Space

2006 ◽  
Vol 46 (3) ◽  
pp. 385-388 ◽  
Author(s):  
Wang Peng ◽  
Fang Jian-Hui ◽  
Zhang Peng-Yu ◽  
Ding Ning
Keyword(s):  
Phase Space ◽  
Variable Mass ◽  
Mechanical Systems

scholarly journals Noether's symmetry and conserved quantity for a time-delayed Hamiltonian system of Herglotz type

2018 ◽  
Vol 5 (10) ◽  
pp. 180208 ◽  
Author(s):  
Yi Zhang
Keyword(s):  
Time Delay ◽  
Phase Space ◽  
Hamiltonian System ◽  
Variational Problem ◽  
Conserved Quantity ◽  
Noether Symmetry ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Special Cases ◽  
The Relationship

The variational problem of Herglotz type and Noether's theorem for a time-delayed Hamiltonian system are studied. Firstly, the variational problem of Herglotz type with time delay in phase space is proposed, and the Hamilton canonical equations with time delay based on the Herglotz variational problem are derived. Secondly, by using the relationship between the non-isochronal variation and the isochronal variation, two basic formulae of variation of the Hamilton–Herglotz action with time delay in phase space are derived. Thirdly, the definition and criterion of the Noether symmetry for the time-delayed Hamiltonian system are established and the corresponding Noether's theorem is presented and proved. The theorem we obtained contains Noether's theorem of a time-delayed Hamiltonian system based on the classical variational problem and Noether's theorem of a Hamiltonian system based on the variational problem of Herglotz type as its special cases. At the end of the paper, an example is given to illustrate the application of the results.

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