Beam physics can be divided into two groups: ray tracing group and Taylor series group.

1) In single pass systems such as spectrometers and electron microscopes, the computational effort is centered on the computation of the Taylor series expansion around a particular orbit, usual the so-called design orbit or optical axis.

2) In multi-pass systems such as rings, one tries to study the stability of the system and excursion away from the so-called design orbit are of interest. For that reason, the validity of a Taylor map is more dubious. It is more appropriate in our view to integrate the trajectory in the old fashion way.

However, even in case 2, the properties around a particular orbit are of interest. In accelerators one may want to know the lattice functions, the chromaticities or even some low order nonlinear distortions in an attempt to understand the motion and to quantify it.

FPP provides automatic tools to extract a map from an integrator and analyze it. The most common analysis tool is the normal form.

Non beam physics applications

3) General maps: sometimes we must deal with general vectorial equations. For that purpose FPP has a type GMAP.