As a common teaching experience, graduate students are often somewhat astonished, and even disappointed, when the teacher starts the lectures on structural dynamics, and related more advanced topics, by reviewing in some detail the fundamentals of vector and analytical mechanics, which deal with discrete and idealized systems, instead of tackling directly the study of real and complicated systems that would impress their imagination and satisfy their legitimate eagerness to deal with engineering problems.

In this respect, the reaction of an experienced engineer is of course the opposite, as his/her satisfaction is great when he/she is successful in reducing the behaviour of a set of interacting complicated structures to that of a few harmonic oscillators, without losing the essential aspects of the real problem. Clearly, it is necessary to acquire first a proper perspective to fully understand that this reduction is the very essence of the modelling process and that models are necessary to analyse real systems of practical interest. Moreover, the discrete models constitute the cornerstone of mathematical modelling, providing the analytical framework and numerical methods used in resolving mechanical engineering problems which can be incredibly complex. It is to these concepts and methods that this first volume is dedicated, while concentrating principally on the linear problems.

Chapter 1 reviews the fundamental concepts and results of Newtonian mechanics. Besides the three founding principles enunciated by Newton, the essential points are first the concept of degrees of freedom (in short DOF) and generalized coordinates and then the formulation of...