scholarly journals On the influence of vertical vibrations on the stability of permanent rotations of a rigid body about axes lying in the main plane of inertia

2017 ◽  
Vol 27 (1) ◽  
pp. 98-120
Author(s):  
E.A. Vishenkova ◽  
◽  
O.V. Kholostova ◽  
◽  
Keyword(s):  
Rigid Body ◽  
Main Plane ◽  
Vertical Vibrations ◽  
The Stability ◽  
Permanent Rotations

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.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers

1975 ◽  
Vol 42 (3) ◽  
pp. 552-556 ◽  
Author(s):  
A. J. Padgaonkar ◽  
K. W. Krieger ◽  
A. I. King
Keyword(s):  
Experimental Data ◽  
Rigid Body ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Theory And Practice ◽  
Body Segments ◽  
Impact Biomechanics ◽  
The Stability ◽  
Definition Of

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.

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