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IssuesArchive of Issues2001-3pp.30-41

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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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