Mathematical study of the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid and a barotropic gas (Oscillations of a pendulum with almost homogeneous liquid and gas)

2011 ◽  
Vol 62 (5) ◽  
pp. 849-868
Author(s):  
H. Essaouini ◽  
L. El Bakkali ◽  
P. Capodanno
Keyword(s):  
Mathematical Study ◽  
Small Oscillations ◽  
Homogeneous Liquid ◽  
Inviscid Liquid ◽  
Barotropic Gas

scholarly journals Mathematical study of the small oscillations of a finite cylindrical column liquid-gas under zero gravity

2019 ◽  
Vol 7 (1) ◽  
pp. 4
Author(s):  
Hilal Essaouini ◽  
Pierre Capodanno
Keyword(s):  
Variational Equation ◽  
Equations Of Motion ◽  
Geometric Condition ◽  
Zero Gravity ◽  
Mathematical Study ◽  
Small Oscillations ◽  
Cylindrical Column ◽  
Barotropic Gas ◽  
Circular Rings ◽  
Classical Vibration

This paper deals with the mathematical study of the small motions of a system formed by a cylindrical liquid column bounded by two parallel circular rings and an internal cylindrical column constituted by a barotropic gas under zero gravity. From the equations of motion, the authors deduce a variational equation. Then, the study of the small oscillations depends on the coerciveness of a hermitian form that appears in this equation. It is proved that this last problem is reduced to an auxiliary eigenvalues problem. The discussion shows that, under a simple geometric condition, the problem is a classical vibration problem.  

Analysis of small oscillations of a heavy almost-homogeneous liquid–gas system

2010 ◽  
Vol 37 (3) ◽  
pp. 337-340 ◽  
Author(s):  
H. Essaouini ◽  
L. El Bakkali ◽  
P. Capodanno
Keyword(s):  
Small Oscillations ◽  
Homogeneous Liquid ◽  
Gas System
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