scholarly journals On the Stability of Pendulum-type Motions in the Approximate Problem of Dynamics of a Lagrange Top with a Vibrating Suspension Point

2018 ◽  
Vol 14 (2) ◽  
pp. 243-263
Author(s):  
M.V. Belichenko ◽  
Keyword(s):  
Suspension Point ◽  
Approximate Problem ◽  
Lagrange Top ◽  
The Stability

scholarly journals On the stability of stationary rotations in the approximate problem of motion of Lagrange’s top with a vibrating suspension point

2017 ◽  
Vol 13 (1) ◽  
pp. 81-104 ◽  
Author(s):  
М.В. Беличенко ◽  
◽  
О.В. Холостова ◽  
Keyword(s):  
Suspension Point ◽  
Approximate Problem ◽  
The Stability

On the Existence of Focus Singularities in One Model of a Lagrange Top with a Vibrating Suspension Point

2020 ◽  
Vol 102 (3) ◽  
pp. 468-471
Author(s):  
A. V. Borisov ◽  
P. E. Ryabov ◽  
S. V. Sokolov
Keyword(s):  
Suspension Point ◽  
Lagrange Top

On the Stability of the rotation under the action of constant momentum Lagrangian top with perfect fluid in a resisting medium

2019 ◽  
Vol 33 ◽  
pp. 122-131
Author(s):  
Yuri Kononov ◽  
Valeriya Vasylenko
Keyword(s):  
Asymptotic Stability ◽  
Solid Body ◽  
Ideal Liquid ◽  
Uniform Rotation ◽  
Ellipsoidal Cavity ◽  
Resisting Medium ◽  
Lagrange Top ◽  
The Stability ◽  
Constant Moment ◽  
The Ideal

The rotation around a fixed point of a heavy dynamically symmetric solid body with an arbitrary asymmetric cavity completely filled with an ideal in-compressible liquid is considered. The stability of a uniform rotation of a Lagrang' top with the ideal liquid in a resisting medium under condition of a given constant moment is investigated. The equation of the perturbed motion of the Lagrang' top with the ideal liquid is presented. It is proved the follow-ing: the asymptotic stability of uniform rotation for an ellipsoidal cavity will be only for a compressed ellipsoidal cavity. It has been observed that most practically important cases consider the main effect of the ideal liquid influence on the motion of a solid can be researched by means of considering only the fundamental tone of the liquid oscillation. Conditions of uniform rotation asymptotic stability in a resistive medium under the action of the Lagrange top' constant moment with an arbitrary axisymmetric cavity containing an ideal liquid are obtained. Stability conditions are derived with provisions for the main and additional tones of liquid oscillations. The heavy solid body with the fixed-point value is ex-posed to the action of a constant moment in the inertial coordinate system. Analytic and numerical investigations of the main and additional tones of liquid oscillations influence, over-turning, restoring, dissipative and constant moments on the conditions of the asymptotic stability of the uniform rotation of the Lagrange top with an ideal liquid are carried out. It is stated the following: cubic and square inequalities presented in the paper are conditions of asymptotic stability if the basic tone of liquid fluctuations will be mentioned. Stability region numerical studies have been carried out on the example of an ellipsoidal cavity. It is presented that increasing of the equatorial moment of inertia of the solid body de-creases its stability region as well as the increasing of the solid body inertia axial moment in-creases the last one.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

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