This first volume is concerned with discrete systems the study of which constitutes the cornerstone of all mechanical systems, linear or non-linear. It covers the formulation of equations of motion and the systematic study of free and forced vibrations. The book goes into detail about subjects such as generalized coordinates and kinematical conditions; Hamiltons principle and Lagrange equations; linear algebra in N-dimensional linear spaces and the orthogonal basis of natural modes of vibration of conservative systems. Also included are the Laplace transform and forced responses of linear dynamical systems, the Fourier transform and spectral analysis of excitation and response deterministic signals. Forthcoming volumes in this series: Vol II: Structural Elements; to be published in June 2005 Vol III: Fluid-structure Interactions; to be published in August 2006 Vol IV: Flow-induced Vibrations; to be published in August 2007 * Presents the general methods that provide a unified framework to model mathematically mechanical systems of interest to the engineer, analyzing the response of these systems * Focuses on linear problems, but includes some aspects of non-linear configuration * Comprehensive coverage of mathematical techniques used to perform computer-based analytical studies and numerical simulations * Discusses the mathematical techniques used to perform analytical studies and numerical simulations on the computer.