Iterative feedback tuning for Hamiltonian systems based on variational symmetry

2019 ◽  
Vol 29 (16) ◽  
pp. 5845-5865 ◽  
Author(s):  
Satoshi Satoh ◽  
Kenji Fujimoto
Keyword(s):  
Hamiltonian Systems ◽  
Iterative Feedback ◽  
Variational Symmetry

scholarly journals Iterative Feedback Tuning for Hamiltonian Systems

2008 ◽  
Vol 41 (2) ◽  
pp. 15678-15683 ◽  
Author(s):  
Kenji Fujimoto ◽  
Ikuo Koyama
Keyword(s):  
Hamiltonian Systems ◽  
Iterative Feedback

Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov
Keyword(s):  
Internal Energy ◽  
Hamiltonian Systems ◽  
Classical Mechanics ◽  
Motion Equation ◽  
Holonomic Constraints ◽  
Dissipative Processes ◽  
Motion Energy ◽  
Analytical Review ◽  
History Of ◽  
Material Points

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

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