Introduction

A knowledge of the rudiments of dynamics is essential to understanding structural dynamics. Thus this chapter reviews the basic theorems of dynamics without any consideration of structural behavior. This chapter is preliminary to the study of structural dynamics because these basic theorems cover the dynamics of both rigid bodies and deformable bodies. The scope of this chapter is quite limited in that it develops only those equations of dynamics, summarized in Section 1.10, that are needed in subsequent chapters for the study of the dynamic behavior of (mostly) elastic structures. Therefore it is suggested that this chapter need only be read, skimmed, or consulted as is necessary for the reader to learn, review, or check on (i) the fundamental equations of rigid/flexible body dynamics and, more importantly, (ii) to obtain a familiarity with the Lagrange equations of motion.

The first part of this chapter uses a vector approach to describe the motions of masses. The vector approach arises from the statement of Newton's second and third laws of motion, which are the starting point for all the material in this textbook. These vector equations of motion are used only to prepare the way for the development of the scalar Lagrange equations of motion in the second part of this chapter. The Lagrange equations of motion are essentially a reformulation of Newton's second law in terms of work and energy (stored work).