The necessary and sufficient condition for the stability of a rigid body
Stability of a rigid body
DOI:
https://doi.org/10.24297/jap.v13i6.6255Keywords:
Rigid body, Lyapunov function, First integrals, Euler-Poisson equationsAbstract
In this paper, the stability of the unperturbed rigid body motion close to conditions, related with the center of mass, is investigated. The three first integrals for the equations of motion are obtained. These integrals are used to achieve a Lyapunov function and to obtain the necessary and sufficient condition satisfies the stability criteria.
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References
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[6] M. P. Guliaev, The stability of rotation of a rigid body with one point fixed in the Euler case, J. Appl. Math. Mech. 23, 2, 579-582, 1959.
[7] Iu. A. Arkhangelskii, On the stability of motion of a heavy solid about a fixed point in a certain special case, J. Appl. Math. Mech. 24, 2, 422-433, 1960.
[8] V. F. Liashenko, On the stability of a rigid body with a fixed point, J. Appl. Math. Mech. 30, 2, 499-502, 1967.
[9] V. D. Irtegov, On the problem of stability of steady motions of a rigid body in a potential force field, J. Appl. Math. Mech. 30, 5, 1113-1117, 1966.
[10] Ye. V. Abrarova, The stability of the steady motions of a rigid body in a central field, J. Appl. Math. Mech. 59, 6, 903-910, 1995.
[11] Yn. N. Kononov, Spin stability of a Lagrange top containing linear oscillators, J. Math. Sci. 103, 1, 2001.
[12] B. S. Bardin, A. A. Savin, The stability of the plane periodic motions of a symmetrical rigid body with a fixed point, J. Appl. Math. Mech. 77, 578-587, 2013.
[13] M. Iñarrea, V. Lanchares, A. I. Pascual, A. Elipe, Stability of the permanent rotations of an asymmetric gyrostat in a Newtonian field, Appl. Math. Comput. 293, 404-415, 2017.
[2] L. Li, On the stability of the rotational motion of a rigid body having a liquid filled cavity under finite initial disturbance, Appl. Math. Mech. 4, 5, 667-680, 1983.
[3] T. V. Rudenko, The stability of the steady motion of a gyrostat with a liquid in a cavity, J. Appl. Math. Mech. 66, 2, 171-178, 2002.
[4] A. V. Karapentyan, V. A. Samaonov, T. S. Sumin, The stability and branching of the permanent rotations of a rigid body with a fluid filling, J. Appl. Math. Mech. 68, 893-897, 2004.
[5] G. K. Pozharitskii, On the stability of permanent rotations of a rigid body with a fixed point under the action of a Newtonian central force field, J. Appl. Math. Mech. 23, 4, 1134-1137, 1959.
[6] M. P. Guliaev, The stability of rotation of a rigid body with one point fixed in the Euler case, J. Appl. Math. Mech. 23, 2, 579-582, 1959.
[7] Iu. A. Arkhangelskii, On the stability of motion of a heavy solid about a fixed point in a certain special case, J. Appl. Math. Mech. 24, 2, 422-433, 1960.
[8] V. F. Liashenko, On the stability of a rigid body with a fixed point, J. Appl. Math. Mech. 30, 2, 499-502, 1967.
[9] V. D. Irtegov, On the problem of stability of steady motions of a rigid body in a potential force field, J. Appl. Math. Mech. 30, 5, 1113-1117, 1966.
[10] Ye. V. Abrarova, The stability of the steady motions of a rigid body in a central field, J. Appl. Math. Mech. 59, 6, 903-910, 1995.
[11] Yn. N. Kononov, Spin stability of a Lagrange top containing linear oscillators, J. Math. Sci. 103, 1, 2001.
[12] B. S. Bardin, A. A. Savin, The stability of the plane periodic motions of a symmetrical rigid body with a fixed point, J. Appl. Math. Mech. 77, 578-587, 2013.
[13] M. Iñarrea, V. Lanchares, A. I. Pascual, A. Elipe, Stability of the permanent rotations of an asymmetric gyrostat in a Newtonian field, Appl. Math. Comput. 293, 404-415, 2017.
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Published
2017-07-13
How to Cite
Amer, W. S. (2017). The necessary and sufficient condition for the stability of a rigid body: Stability of a rigid body. JOURNAL OF ADVANCES IN PHYSICS, 13(6), 4999–5003. https://doi.org/10.24297/jap.v13i6.6255
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