Classical dynamics of systems with time-varying inertial properties with application to multi-rigid body systems

This thesis describes an investigation into the classical dynamics of systems with time-varying inertial properties, and is believed to be the only comprehensive treatment of this topic to be found in the literature at present. The "inertial properties" of a system are mathematically represented by the total mass plus the center of mass location and inertia tensor, calculated with respect to some point associated with the system. Obviously, these properties are varying if the system is capturing or releasing mass. The term "variable-mass" is used to designate such systems. Even for a constant-mass system however, the inertial properties can vary due to changes in its internal or external configuration.

A general and systematic procedure for formulating the equations of motion for these systems is developed. The first step in this procedure is to identify the time-varying mass of interest using a control volume that can translate, rotate, and deform with the system. The second step is to apply to this control volume a set of general motion equations that have been presented in this thesis. Some of these control-volume equations can be found scattered throughout the literature, while some represent new results. The important contribution of this research is the organization of these equations into a unified and self-consistent dynamic theory.

A second significant contribution is a vector-dyadic formulation of the equations of motion for a variable-mass multibody system. This system has been modelled as a constant number of rigid bodies plus a time-varying number of particle masses, all executing known motions relative to an unconstrained rigid base body. The governing equations reflect the time-varying nature of the system's inertial properties, and have been encoded into a computer program. The orientation of each rigid body has been represented using the "conformal rotation vector", a set of three parameters that offers several computational advantages. Using a fourth-order Runge-Kutta algorithm, the program can numerically integrate the nonlinear equations of motion for a particular multibody system. The application of this user-friendly code to the dynamic analyses of several physical systems is demonstrated.