Geodesic
Cases of integrability corresponding to the pendulum motion in four-dimensional space
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 41-58

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In this article, we systemize some results on the study of the equations of motion of dynamically symmetric fixed four-dimensional 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 the motion of a free four-dimensional 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. We also show the nontrivial topological and mechanical analogies.
Keywords: four-dimensional rigid body, non-conservative force field, dynamical system, case of integrability. 
@article{VSGU_2017_1_a4,
     author = {M. V. Shamolin},
     title = {Cases of integrability corresponding to the pendulum motion in four-dimensional space},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {41--58},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2017_1_a4/}
}
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M. V. Shamolin. Cases of integrability corresponding to the pendulum motion in four-dimensional space. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 41-58. http://geodesic.mathdoc.fr/item/VSGU_2017_1_a4/