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

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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A Note on the Stability of Permanent Rotations of a Heavy Rigid Body With a Fixed Point

Journal of Applied Mechanics ◽

10.1115/1.3423536 ◽

1975 ◽

Vol 42 (1) ◽

pp. 239-240

Author(s):

D. J. McGill ◽

L. S. Long

Keyword(s):

Fixed Point ◽

Rigid Body ◽

Heavy Rigid Body ◽

The Stability ◽

Permanent Rotations

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On the stability of the permanent rotations of a rigid body about a fixed point in Brun's problem

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(94)90019-1 ◽

1994 ◽

Vol 58 (5) ◽

pp. 927-931

Author(s):

M.A. Novikov

Keyword(s):

Fixed Point ◽

Rigid Body ◽

The Stability ◽

Permanent Rotations

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

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(59)90049-8 ◽

1959 ◽

Vol 23 (4) ◽

pp. 1134-1137 ◽

Cited By ~ 2

Author(s):

G.K Pozharitskii

Keyword(s):

Fixed Point ◽

Rigid Body ◽

Force Field ◽

Central Force ◽

Central Force Field ◽

The Stability ◽

Permanent Rotations

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On the Stability of Plane Motion of Heavy Rigid Body about a Fixed Point

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.19870671214 ◽

1987 ◽

Vol 67 (12) ◽

pp. 641-648 ◽

Cited By ~ 5

Author(s):

H. M. Yehia

Keyword(s):

Fixed Point ◽

Rigid Body ◽

Plane Motion ◽

Heavy Rigid Body ◽

The Stability

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The Stability of Motion of a Rigid Body About a Fixed Point in the Case of Euler With Damping Torque

Journal of Applied Mechanics ◽

10.1115/1.3167570 ◽

1984 ◽

Vol 51 (1) ◽

pp. 198-199 ◽

Cited By ~ 1

Author(s):

Z.-M. Ge ◽

X.-X. Wu

Keyword(s):

Fixed Point ◽

Rigid Body ◽

Stability Of Motion ◽

The Stability ◽

Damping Torque

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THE STABILITY OF MOTION OF A RIGID BODY ABOUT A FIXED POINT IN THE CASE OF EULER WITH VARIOUS DAMPING TORQUES

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1988-0024 ◽

1988 ◽

Vol 12 (3) ◽

pp. 165-171

Author(s):

Z.M. GE ◽

M.H. WU

Keyword(s):

Fixed Point ◽

Rigid Body ◽

Direct Method ◽

Time Varying ◽

Stability Of Motion ◽

Fixed Orientation ◽

Non Linear Systems ◽

The Stability ◽

Damping Torque ◽

Liapunov's Direct Method

The stabilities of motion of a rigid body about a fixed point around a fixed orientation in space with damping torque are studied in thirteen cases. The problems involve stabilities of time-varying solutions of non-autonomous non-linear systems. By using Liapunov’s direct method, many interesting results are obtained.

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THE STABILITY OF THE UNSYMMETRICAL HEAVY GYRO WITH DAMPING TORQUE

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1992-0006 ◽

1992 ◽

Vol 16 (1) ◽

pp. 83-89

Author(s):

Zheng-Ming E ◽

Shih-Ming Chiu

Keyword(s):

Fixed Point ◽

Rigid Body ◽

Direct Method ◽

Nonlinear Damping ◽

Center Of Gravity ◽

Moments Of Inertia ◽

Principal Moments Of Inertia ◽

The Stability ◽

Damping Torque

The conditions of the unsymmetrical heavy gyro are that A ≠ B ≠ C where, A, B and C are the principal moments of inertia of the rigid body and the center of gravity G of the rigid body does not coincide with the fixed point, i.e. zc ≠ 0, xc = yc = 0 in this paper. The conditions of the stability and of the instability of the unsymmetrical heavy gyro with and without linear or nonlinear damping torque are obtained by the direct method of Lyapunov.

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