This research project deals with an in-depth analysis of rotating mechanical systems. Such systems are modelled by ordinary differential equations with periodically varying coefficients. The models are very often high-dimensional, possess non-linearities that cannot be neglected, and depend on many widely varying design parameters. The point-mapping based methodology used in this research combines the advantages of analytical methods that allow qualitative analysis and the ability of numerical methods to analyze high-order systems with parameters varying over a large range. The point mapping approach results in an analytical representation of discrete-time dynamics of the rotating system. The equations for steady-state solutions, conditions of stability and bifurcation of these solutions, and sensitivity of the system's behavior to design parameters are formulated in terms of closed-form algebraic equations. The analytical formulation allows design tradeoffs to be performed using computer algebra. The research includes development and implementation of the theoretical and computational aspects of the point mapping based methodology, and study of important classes of rotating systems. In each application, a detailed sensitivity and design tradeoff analysis as a function of system parameters is performed using high-speed computation algorithms. +?+¬ ó ¬ñ«¬^áúú¬^Ñ¿«ñ +?+¬ ó ¬ñ«¬^áúú¬^½¿? +?+¬
