Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space

Author:

Shamolin Maxim V.1

Affiliation:

1. Lomonosov Moscow State University Institute of Mechanics Michurinskii Ave., 1, 119192 Moscow, Russian Federation

Abstract

We systematize some results on the study of the equations of spatial motion of dynamically 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 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

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

Mechanical Engineering,Mechanics of Materials,General Materials Science

Reference17 articles.

1. Shamolin M. V. Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium, J. Math. Sci., 2002, 110, no. 2, pp. 2526–2555.

2. Shamolin M. V. New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium, J. Math. Sci., 2003, 114, no. 1, pp. 919–975.

3. Shamolin M. V. Foundations of differential and topological diagnostics, J. Math. Sci., 2003, 114, no. 1, pp. 976–1024.

4. Shamolin M. V. Classes of variable dissipation systems with nonzero mean in the dynamics of a rigid body, J. Math. Sci., 2004, 122, no. 1, pp. 2841–2915.

5. Shamolin M. V. On integrability in elementary functions of certain classes of nonconservative dynamical systems, J. Math. Sci., 2009, 161, no. 5, pp. 734–778.

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