Geodesic
On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2017), pp. 41-64

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In the proposed cycle of work, we study the equations of the motion of dynamically symmetric fixed $n$-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 $n$-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. In thit work, we derive the general multi-dimensional dynamic equations of the systems under study.
Keywords: multi-dimensional rigid body, non-conservative force field, dynamical system, case of integrability. 
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     author = {M. V. Shamolin},
     title = {On a pendulum motion in multi-dimensional space. {Part} 1. {Dynamical} systems},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {41--64},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2017_3_a5/}
}
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M. V. Shamolin. On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2017), pp. 41-64. http://geodesic.mathdoc.fr/item/VSGU_2017_3_a5/