Geodesic
Cases of integrability corresponding to the pendulum motion in three-dimensional space
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3-4 (2016), pp. 75-97

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In this actitity, we systemize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies-pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.
Keywords: rigid body, resisting medium, dynamical system, three-dimensional phase pattern, case of integrability. 
@article{VSGU_2016_3-4_a6,
     author = {M. V. Shamolin},
     title = {Cases of integrability corresponding to the pendulum motion in three-dimensional space},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {75--97},
     publisher = {mathdoc},
     number = {3-4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a6/}
}
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M. V. Shamolin. Cases of integrability corresponding to the pendulum motion in three-dimensional space. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3-4 (2016), pp. 75-97. http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a6/