WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 12, 2017
Cases of Integrability Corresponding to the Motion of a Pendulum on the Two-Dimensional Plane
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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.
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Keywords: Rigid body, Pendulum, Resisting Medium, Dynamical SystemsWith Variable Dissipation, Integrability
Pages: 123-135
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 12, 2017, Art. #16