 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. K. Alekhin, "On the stability of plane motions of a heavy axially symmetric rigid body," Mech. Solids. 41 (4), 40-45 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
4 |
Pages |
40-45 |
| Title |
On the stability of plane motions of a heavy axially symmetric rigid body |
| Author(s) |
A. K. Alekhin (Moscow) |
| Abstract |
We consider the motion of a rigid body with one fixed point in a
homogeneous gravitational field. We assume that the ellipsoid of inertia of
the body about the fixed point is an ellipsoid of revolution.
We study the orbital stability of plane periodic motions of the body. In
the unperturbed motion, the body oscillates or rotates around the axis of
symmetry, which is always horizontal. The oscillation amplitude or the
rotation frequency of the body is arbitrary.
We show that the problem depends on the following two parameters: the ratio
of the nonequal principal moments of inertia and the energy constant in the
unperturbed motion, which determines the oscillation amplitude or the
rotation frequency.
In the plane of these parameters, we construct orbital stability and
instability domains in the first (linear) approximation. We also perform
nonlinear analysis of orbital stability in the stability domains in the
first approximation and on their boundaries. |
| References |
| 1. | A. P. Markeev,
"On area-preserving mappings and their application in dynamics
of systems with impacts,"
Izv. RAN. MTT [Mechanics of Solids], No. 2, pp. 37-54, 1996. |
| 2. | A. P. Markeev,
"Stability of equilibrium states of
hamiltonian systems: a method of investigation,"
Izv. RAN. MTT [Mechanics of Solids], No. 6, pp. 3-12, 2004. |
| 3. | A. P. Markeev, "On stability of plane motions of a rigid body in
the Kovalevskaya case," PMM [Applied Mathematics and Mechanics], Vol. 65,
No. 1, pp. 51-58, 2001. |
| 4. | A. P. Markeev,
"On pendulum-like motions of a rigid body
in the Goryachev-Chaplygin case,"
PMM [Applied Mathematics and Mechanics], Vol. 68, No. 2, pp. 282-293, 2004. |
|
| Received |
10 August 2004 |
| << Previous article | Volume 41, Issue 4 / 2006 | Next article >> |
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