In this chapter, we will explore some aspects of mathematical model of
glider flight. This model is called Lanchester's
*phugoid theory*^{3.1}, developed by Frederick Lanchester [Lan] at
beginning of the twentieth century.
While this model has its drawbacks, it still is used today to
explain oscillations and stalls in airplane flight.

Since this model, like many models, is a set of differential equations, we will need some results which are typically covered in a course on differential equations. We will cover the relevant material briefly here, but readers needing a more in-depth treatment are encouraged to look in a text on ordinary differential equations, such as [BDH], [HW], or [EP]. Of these, the approach in [BDH] is perhaps closest to the one presented here.

- ... theory
^{3.1} - Folklore has it that this name was
chosen by Lanchester because he wanted a classically-based name for his
new theory of oscillations occuring during flight. Since the Greek root
*phug*( , pronounced ``fyoog'') as well as the Latin root*fug-*both correspond to the English word ``flight'', he decided on the name ``phugoid''. Unfortunately, in both Greek and Latin, this means ``flight'' as in ``run away'' instead of what birds and airplanes do-- the same root gives rise to the words ``fugitive'' and ``centrifuge''. The Latin for flight in appropriate sense is*volatus*; the Greek word is*potê*(*o*).

- The Phugoid model
- What do solutions look like?
- Existence of Solutions
- Numerical Methods

- Seeing the flight path
- Fixed Point Analysis

- Qualitative Classification of Solutions
- Dealing with the Singularity

2002-08-29