NonlinearNormalForm

Overview

This package is still in an early development stage

This package provides routines for calculating parameter-dependent normal forms of nonlinear Hamiltonian (and nearly Hamiltonian) maps expressed as truncated power series in the variables, using Lie algebraic methods. Basically, given some map, it computes a symplectic transformation of the variables to coordinates where the nonlinear motion lies on circles in phase space. This allows calculation of invariants of the motion, and when leaving one resonance in the map, a single-resonance normal form, from which resonance driving terms can be calculated. This package may be of particular interest to those in accelerator physics, electron microscopy, and astronomy.

Setup

To use this package, in the Julia REPL run:

import Pkg; Pkg.add(path="https://github.com/bmad-sim/NonlinearNormalForm.jl")

Basic Usage

This package imports and reexports GTPSA.jl, a library for computing real and complex truncated power series to arbitrary orders in the variables and parameters. Before using NonlinearNormalForm.jl, you should have some familiarity with GTPSA.jl.