Cartesian Tensors and Rigid Body Motion

Abstract

As we have mentioned in Chapter 1, the representation of the physical quantities involved in the formulation of the equations of motion of a rigid body system determines the kind of mathematical analysis that will be used in deriving these equations. In the classical Newtonian formulation of rigid body dynamics, vectors are usually used [1-5] to represent basic physical quantities and therefore vector analysis is used for deriving the equations of rigid body motion. Vector analysis is usually imposed on classical Newtonian dynamics by the consideration that angular rates (i.e., linearly independent rates of change of a rigid body orientation) constitute the components of a vector quantity, the angular velocity vector. This consideration also assigns a vector character to other physical quantities which are defined in terms of the angular velocity vector such as angular acceleration, angular momentum and external torque. However, as is well known [9], basic physical quantities in rigid body motion such as angular velocity, angular acceleration, angular or rotational momentum and resultant torque can be described by using second order Cartesian tensors. Therefore, based on the Cartesian tensor representation of these quantities, we can use Cartesian tensor analysis for the study of rigid body motion