On the stability of permanent rotations of a rigid body with a fixed point under the action of a Newtonian central force field

1959 ◽  
Vol 23 (4) ◽  
pp. 1134-1137 ◽  
Author(s):  
G.K Pozharitskii
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Force Field ◽  
Central Force ◽  
Central Force Field ◽  
The Stability ◽  
Permanent Rotations

STABILITY OF EULER, LAGRANGE AND KOVALEVSKAYA GYROS IN A NEWTONIAN CENTRAL FORCE FIELD WITH SECOND ORDER TERMS

1996 ◽  
Vol 20 (1) ◽  
pp. 41-53
Author(s):  
Zheng-Ming Ge ◽  
Fu-Neng Ku
Keyword(s):  
Fixed Point ◽  
Force Field ◽  
Direct Method ◽  
High Accuracy ◽  
Second Order ◽  
Central Force ◽  
Central Force Field ◽  
Liapunov Direct Method ◽  
Permanent Rotation ◽  
The Stability

The stability of the permanent rotation of the Euler, Lagrange and Kovalevskaya gyros about a fixed point in the Newtonian central force field is investigated by Liapunov direct method, which improve Leimanis’ and Rumiantsev’s result of stability conditions. For the sake of high accuracy, the first and second order terms of R-1 expressed by potential energy of the Newtonian central force field have been considered, where the R is the distance from the fixed point to the center of attraction.

On Nonholonomic Parametrization

1970 ◽  
Vol 37 (1) ◽  
pp. 128-132
Author(s):  
B. Vujanovic
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Fixed Point ◽  
Rigid Body ◽  
Force Field ◽  
First Integral ◽  
Central Force Field ◽  
The Stability ◽  
Asymmetric Rigid Body ◽  
System Time

This paper is concerned with the problem of obtaining the differential equation of the trajectory of dynamical system. Time is eliminated by means of some first integral linear with respect to the velocities. As an example, the stability of rotation of a heavy asymmetric rigid body with a fixed point under the action of the Newtonian central force field is considered.

Another Theorem for Determining the Definiteness of Sign of Functions and Its Applications to the Stability of Permanent Rotations of a Rigid Body

1984 ◽  
Vol 51 (2) ◽  
pp. 430-434 ◽  
Author(s):  
Z.-M. Ge ◽  
Y.-J. Wu
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
The Stability ◽  
Permanent Rotations

A new theorem for determining the definiteness of sign of functions is presented. As the examples illustrate, it is applied to the stability of permanent rotations of a rigid body about a fixed point in five cases.

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