TABLE OF CONTENTS This chapter is intended both as a review of the basic principles of the Newtonian mechanics and as an introduction to a few physical concepts and mathematical notations we shall use throughout the book. Here, equilibrium equations (dynamic or static) of discrete systems are still derived by using the vector mechanics, i.e. direct balancing of the forces, and/or moments acting in the system. This approach is certainly the most familiar one to the majority of students, who are assumed to be already well acquainted with the basic techniques of vector analysis of Newtonian mechanics. However, the notions emphasized here, which concern degrees of freedom, generalized coordinates and kinematical conditions, are the first necessary ingredients of the Lagrangian formalism which is the subject of the next three chapters. Although the physical content of analytical mechanics founded by Lagrange (1788) is the same as that found in the Principia of Newton (1687), the analytical approach is more appealing from the logical viewpoint than the vectorial one and, even if more abstract, quickly reveals itself as far easier to apply when dealing with most material systems encountered in theoretical physics and mechanical engineering.
Formulation of a mathematical model is the first step in the process of analysing the behaviour of any real system. However, to produce a useful model, one must first adopt a set of simplifying assumptions which have to be relevant in relation to the physical features of the system to...
