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Conference Proceedings
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8th International Conference on Physics and Control (PhysCon 2017)
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Cases of integrability corresponding to the motion of a pendulumin the three-dimensional space
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We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodiesâ€“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, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system.