Stability regions for an unsymmetrical rigid body spinning about an axis through a fixed point

1975 ◽  
Vol 22 (1-2) ◽  
pp. 91-112 ◽  
Author(s):  
D. J. McGill ◽  
L. S. Long
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Stability Regions

Chaos in a restricted problem of rotation of a rigid body with a fixed point

2008 ◽  
Vol 13 (3) ◽  
pp. 221-233 ◽  
Author(s):  
A. V. Borisov ◽  
A. A. Kilin ◽  
I. S. Mamaev
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Restricted Problem

Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 293-302
Author(s):  
Ivan Polekhin
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Integrable Case ◽  
Analytical Results ◽  
Routh Reduction ◽  
Gyroscopic Forces ◽  
Kovalevskaya Case

AbstractThe problem of motion of a rigid body with a fixed point is considered. We study qualitatively the solutions of the system after Routh reduction. For the Lagrange integrable case, we show that the trajectories of solutions starting at the boundary of a possible motion area can both cover and not cover the entire possible motion area. It distinguishes these systems from the systems without gyroscopic forces, where the trajectories always cover the possible motion area. We also present some numerical and analytical results on the same matter for the Kovalevskaya case.

scholarly journals On the dynamics of the rigid body with a fixed point: periodic orbits and integrability

2013 ◽  
Vol 74 (1-2) ◽  
pp. 327-333 ◽  
Author(s):  
Juan L. G. Guirao ◽  
Jaume Llibre ◽  
Juan A. Vera
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Periodic Orbits

Rotations of a Rigid Body About a Fixed Point

1945 ◽  
Vol 13 (3) ◽  
pp. 137-140 ◽  
Author(s):  
E. L. Hill
Keyword(s):  
Fixed Point ◽  
Rigid Body

The Stress-Strain Analysis for the Nonlinear and Strength Difference Structure of Bars Jointed to Rigid-Body of Fixed-Point Motion

2010 ◽  
Vol 156-157 ◽  
pp. 383-386
Author(s):  
Xie Quan Liu ◽  
Xin Hua Ni ◽  
Shu Qin Zhang ◽  
Lei Zhao ◽  
Guo Hui Zhong
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Angular Displacement ◽  
Strain Analysis ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Point Motion ◽  
Tension And Compression ◽  
Strength Difference

Many material have different stress-strain relation in tension and compression, generally the relation is nonlinear. In this paper, we use two exponential functions to approximately represent the stress-strain relation of nonlinearly elastic material and analyze strength-difference structure of bars jointed to Rigid-body of fixed-point motion. The displacement method is used to derive the universal expression of calculating stress and strain. The nonlinear equations for computing angular displacement of the rigid-body has been given and general computing program has been worked out. They can be accurately and conveniently calculated. This problem has been solved satisfactorily.

scholarly journals 2. On the Rotation of a Rigid Body about a Fixed Point

1869 ◽  
Vol 6 ◽  
pp. 430-434
Author(s):  
Tait
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Mutual Relations

This paper contains an attempt to exhibit the mutual relations of some of the more important of the various processes which have been employed in solving one of the most celebrated problems of Dynamics. The Quaternion analysis has been throughout used, as far more briefly comprehensive and more suggestively expressive than the ordinary Cartesian analysis.

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