Geodesic
Cases of integrability corresponding to the pendulum motion on the plane
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 91-113

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In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconservative force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. 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, phase pattern, case of integrability. 
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     author = {M. V. Shamolin},
     title = {Cases of integrability corresponding to the pendulum motion on the plane},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {91--113},
     publisher = {mathdoc},
     number = {10},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_10_a7/}
}
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M. V. Shamolin. Cases of integrability corresponding to the pendulum motion on the plane. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 91-113. http://geodesic.mathdoc.fr/item/VSGU_2015_10_a7/