The notations in this book are not uniform; this is partly done on purpose and partly because we had no choice. Indeed modelers usually have to comply or at least adapt to the notations common in a given field, and thus they must be trained to some flexibility. Another reason for having non-uniform notations is that different fields are present in this volume, and it was not possible to find notations fitting all the standards.

Another objective while deciding the notations was to choose notations that can be easily reproduced by handwriting, thus avoiding as much as possible arrows, boldfaced type, and simple and double underlining with bars or tildes; in general, in a given chapter of this book, in a given context, it is clear what a given symbol represents.

Although the notations are not rigid, there are still some repeated patterns in the notations, and we indicate hereafter notations used in several chapters:

? or , possibly with indices: domain in ² or ³

x = ( x ₁, x ₂) or ( x ₁, x ₂, x ₃): generic point in ² or ³. Also denoted ( x, y) or ( x, y, z)

a = ( a ₁, a ₂) or ( a ₁, a ₂, a ₃): initial position in Lagrangian variables

t: time

u = ( u ₁, u ₂