Equations of Motion of an Ideal Incompressible Fluid; Kelvin’s Circulation Theorem

2013 ◽  
pp. 3-11
Author(s):  
Felix V. Dolzhansky
Keyword(s):  
Incompressible Fluid ◽  
Equations Of Motion ◽  
Ideal Incompressible Fluid ◽  
Circulation Theorem

scholarly journals Non-Linear Oscillations and Beats in the Beta Canis Majoris Stars

1993 ◽  
Vol 134 ◽  
pp. 73-76
Author(s):  
A. S. Baranov
Keyword(s):  
Incompressible Fluid ◽  
Equatorial Plane ◽  
Equations Of Motion ◽  
Critical Evaluation ◽  
Oscillation Theory ◽  
Ideal Incompressible Fluid ◽  
Equilibrium Figure ◽  
Theory Analysis ◽  
Oscillation Modes ◽  
Non Linear

Notwithstanding a great number of hypotheses, suggested for explaining superpositions of the light- and of the velocity variations of the ß Canis Majoris stars, no one of these does it satisfactorily. Possibly it is due to an inadequate elaboration of the non-linearly oscillation theory. Analysis and critical evaluation of the existing hypotheses are given by Mel’nikov and Popov (1970). Our explanation consists in existence of close frequencies corresponding to various oscillation modes which are non-linearly interacting.Equations of motion of an ideal incompressible fluid under condition of preserving the equilibrium figure symmetry with respect to the equatorial plane (lateral oscillations) have the form (Baranov 1988):

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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