Emmy Noether is recognized as one of the greatest mathematicians of the twentieth century. She was born in Germany in 1882 to an intellectual Jewish family and died in the United States in 1935. Emmy trained as a language teacher, but after passing the qualifying exams to teach, she decided to study mathematics at the University of Erlangen. At that time in Germany a university education was limited to men, although women were allowed to attend classes if given permission by the professor. (She was half of the total female student body at that university.) She spent a semester at the University of Gottingen, at that time a world leader in mathematics and physics. There she attended lectures from a number of leading mathematicians, including Hermann Minkowski (who you will run into in Chapter 20) and Karl Schwarzschild (whose theory of black holes you will encounter in Chapter 9).

This chapter and the next are a study of the general motion of a rigid body. This is a fairly complicated topic which involves mathematical concepts that you may not have encountered before.

I denoted this chapter as “optional” because it contains essentially no new physics. However, it does introduce some useful mathematical concepts and techniques. The methods introduced here are applied in several areas of physics including quantum mechanics and solid-state physics.

This book has concentrated on “integrable” problems, that is, problems whose equations of motion can be integrated yielding closed-form solutions.

As you will soon appreciate, the physics of a pendulum is much more complex than you might imagine.

In this chapter we consider the basic concepts of the statics and dynamics of fluids. As the name indicates, a fluid is any substance that flows, such as liquids and gases. The general categories of our study are fluid statics or hydrostatics concerning the behavior of fluids at rest, and fluid dynamics which is a study of the motion of fluids and of objects moving with respect to fluids. This is further subdivided into studies of the dynamics of liquids and gases or hydrodynamics and gas dynamics.

Classical field theory is primarily a study of electromagnetic and gravitational fields. This chapter is an introduction to field theory and is limited to a few aspects of the gravitational field.

This chapter treats several advanced concepts in statics, well beyond the brief summary of statics in Section 1.6. We will begin with a few definitions and two simple theorems concerning systems of forces acting on rigid bodies, then go on to analyze the statics of freely deformable bodies such as a string or cable hanging from stationary supports. This is followed by definitions of stress and strain and a generalization of Hooke’s law. The last topic is d’Alembert’s principle and the concept of virtual work. You will see how this principle can be used to derive Lagrange’s equations. An important application is an investigation of the properties of a fluid in equilibrium (hydrostatics), but we will leave that for Chapter 19 where we consider fluids in general.