An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

2000 ◽  
Vol 35 (1) ◽  
pp. 24-32 ◽  
Author(s):  
G. Ya. Dynnikova
Keyword(s):  
Incompressible Fluid ◽  
Vortex Flow ◽  
Ideal Incompressible Fluid ◽  
Time Dependent

scholarly journals Weak Dual Pairs and Jetlet Methods for Ideal Incompressible Fluid Models in $$n \ge 2$$ n ≥ 2 Dimensions

2016 ◽  
Vol 26 (6) ◽  
pp. 1723-1765 ◽  
Author(s):  
C. J. Cotter ◽  
J. Eldering ◽  
D. D. Holm ◽  
H. O. Jacobs ◽  
D. M. Meier
Keyword(s):  
Incompressible Fluid ◽  
Ideal Incompressible Fluid ◽  
Fluid Models ◽  
Dual Pairs

scholarly journals On the integrable deformations of a system related to the motion of two vortices in an ideal incompressible fluid

2019 ◽  
Vol 29 ◽  
pp. 01015 ◽  
Author(s):  
Cristian Lăzureanu ◽  
Ciprian Hedrea ◽  
Camelia Petrişor
Keyword(s):  
Incompressible Fluid ◽  
Mechanical System ◽  
Integrable Systems ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Ideal Incompressible Fluid ◽  
First Integrals ◽  
Integrable Deformation ◽  
Integrable Deformations ◽  
The Given

Altering the first integrals of an integrable system integrable deformations of the given system are obtained. These integrable deformations are also integrable systems, and they generalize the initial system. In this paper we give a method to construct integrable deformations of maximally superintegrable Hamiltonian mechanical systems with two degrees of freedom. An integrable deformation of a maximally superintegrable Hamiltonian mechanical system preserves the number of first integrals, but is not a Hamiltonian mechanical system, generally. We construct integrable deformations of the maximally superintegrable Hamiltonian mechanical system that describes the motion of two vortices in an ideal incompressible fluid, and we show that some of these integrable deformations are Hamiltonian mechanical systems too.

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