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Mathematical Problems in Engineering
Volume 2011, Article ID 351269, 26 pages
http://dx.doi.org/10.1155/2011/351269
Research Article

Vector Rotators of Rigid Body Dynamics with Coupled Rotations around Axes without Intersection

1Mathematical Institute, SANU, 11001 Belgrade, Serbia
2Faculty of Mechanical Engineering, University of Kragujevac, 34000 Kragujevac, Serbia

Received 27 January 2011; Revised 30 May 2011; Accepted 1 June 2011

Academic Editor: Massimo Scalia

Copyright © 2011 Katica R. (Stevanović) Hedrih and Ljiljana Veljović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Vector method based on mass moment vectors and vector rotators coupled for pole and oriented axes is used for obtaining vector expressions for kinetic pressures on the shaft bearings of a rigid body dynamics with coupled rotations around axes without intersection. Mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis are defined by K. Hedrih in 1991. These kinematical vectors rotators are defined for a system with two degrees of freedom as well as for rheonomic system with two degrees of mobility and one degree of freedom and coupled rotations around two coupled axes without intersection as well as their angular velocities and intensity. As an example of defined dynamics, we take into consideration a heavy gyrorotor disk with one degree of freedom and coupled rotations when one component of rotation is programmed by constant angular velocity. For this system with nonlinear dynamics, a series of tree parametric transformations of system nonlinear dynamics are presented. Some graphical visualization of vector rotators properties are presented too.