 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| N. N. Bolotnik, "Free motion of a rigid body on a two-degree-of-freedom joint with non-perpendicular axes," Mech. Solids. 36 (3), 30-41 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
3 |
Pages |
30-41 |
| Title |
Free motion of a rigid body on a two-degree-of-freedom joint with non-perpendicular axes |
| Author(s) |
N. N. Bolotnik (Moscow) |
| Abstract |
The motion of a rigid body attached to a fixed base by means
of a two-degree-of-freedom joint is investigated. The fixed and
the movable axes of the joint may form an arbitrary angle. No external
force fields act on the body during its motion. The angle of rotation
of the plane formed by the joint's axes and the angle of rotation
of the body about the movable axis are taken to be the generalized
coordinates. The former of these coordinates is cyclic, while the latter
is positional (i.e., explicitly occurs in the expression for
the kinetic energy). All stationary motions of the system are found
and their stability is analyzed. A classification of motions
with respect to the positional coordinate is given. The properties
of these motions, as well as those of some non-stationary motions
with respect to the cyclic coordinate, are studied.
It is established that the number of different positions of the body
relative to the plane formed by the joint axes in the stationary
motion can vary from two to four, depending on the angle between
the axes and the relationship between the components of the body's
tensor of inertia. The present paper is a generalization of the research
of [1] where free motion of a rigid body on a two-degree-of-freedom
joint with perpendicular axes has been studied. The motion of a rigid body
on a two-degree-of-freedom joint with perpendicular axes in the uniform
gravity field has been investigated in [2]. |
| References |
| 1. | N. N. Bolotnik, "On the free motion of a rigid body
on a single-degree-of-freedom joint," PMM [Applied Mathematics
and Mechanics], Vol. 58, No. 5, pp. 83-90, 1994. |
| 2. | N. N. Bolotnik, "The motion of a rigid body
on a single-degree-of-freedom joint
in the uniform gravity field," PMM [Applied Mathematics
and Mechanics], Vol. 59, No. 6, pp. 908-915, 1995. |
| 3. | A. P. Markeev, Theoretical Mechanics [in Russian],
Nauka, Moscow, 1990. |
| 4. | L. A. Pars, Analytical Dynamics [Russian translation],
Nauka, Moscow, 1971. |
| 5. | A. A. Andronov, A. A, Vitt, and S. E. Khaikin,
Theory of Oscillations [in Russian], Nauka, Moscow, 1981. |
|
| Received |
29 March 1999 |
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