TABLE OF CONTENTS KEY FEATURES
The key features of this chapter are the energy principle for a multi-particle system, the poten tial energies arising from external and internal forces, and energy conservation.
This is the first of three chapters in which we study the mechanics of multi-particle systems. This is an important development which greatly increases the range of problems that we can solve. In particular, multi-particle mechanics is needed to solve problems involving the rotation of rigid bodies.
The chapter begins by obtaining the energy principle for a multi-particle system. This is the first of the three great principles of multi-particle mechanics [*] that apply to every mechanical system without restriction. We then show that, under appropriate conditions, the total energy of the system is conserved. We apply this energy conservation principle to a wide variety of systems. When the system has just one degree of freedom, the energy conservation equation is sufficient to determine the whole motion.
[*] The other two are the linear momentum and angular momentum principles.
A multi-particle system 
may consist of any number of particles P 1, P 2, , P N, with masses m 1, m 2 , m
