AUTHORS: Maxim V. Shamolin
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ABSTRACT: We systematize some results on the study of the equations of plane-parallel motion of 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 plane-parallel 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.
KEYWORDS: Rigid body, Pendulum, Resisting Medium, Dynamical SystemsWith Variable Dissipation, Integrability
REFERENCES:
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[8] Trofimov V. V., and Shamolin M. V. Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems, J. Math. Sci., 2012, 180, no. 4, pp. 365–530.
[9] Shamolin M. V. Comparison of complete integrability cases in Dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field, J. Math. Sci., 2012, 187, no. 3, pp. 346–459.
[10] Shamolin M. V. Some questions of qualitative theory in dynamics of systems with the variable dissipation, J. Math. Sci., 2013, 189, no. 2, pp. 314–323.
[11] Shamolin M. V. Variety of Integrable Cases in Dynamics of Low- and Multi-Dimensional Rigid Bodies in Nonconservative Force Fields, J. Math. Sci., 2015, 204, no. 4, pp. 479–530.
[12] Shamolin M. V. Classification of Integrable Cases in the Dynamics of a Four-Dimensional Rigid Body in a Nonconservative Field in the Presence of a Tracking Force, J. Math. Sci., 2015, 204, no. 6, pp. 808–870.
[13] Shamolin M. V. Some Classes of Integrable Problems in Spatial Dynamics of a Rigid Body in a Nonconservative Force Field, J. Math. Sci., 2015, 210, no. 3, pp. 292–330.
