Integrators

An integrator is a section of code which is capable of approximating the evolution x(t) given the initial conditions x(0) and v(0). Different integrators have different strengths and weaknesses. The purpose of Fraser & Schonrich 2021 was to investigate the differences between the integrators provided below.

We provide three classes along an inheritance chain to aid in these calculations. The Integrator class provides the basic framework of an integrator, including the main evolution loop and the procedures for saving information to file etc. The Magi integrator is a generalised subclass of Integrator for the case of rotating systems without nice symmetry properties, and numerically computes a truncated form of the Magnus series. The Symi integrator in turn subclasses Magi and overloads the Magnus series computation to the exact analytical expressions for axisymmetric systems.

Classes:

• Integrator Superclass
• Magi Integrator
• Symi Integrator

Integrator Enums

Both the Magi and Symi classes can undergo different step-types, determining how they move from \(\mathsf{q}_{i+1} \to \mathsf{q}_i\). The relevant classes determine which of these to used based on the template argument, UpdateType.

enum QDynamics::UpdateType

Values:

enumerator Brute

The dumbest way to update the formula, directly evaluates linear update formula. Note that Brute integrators do not compute the Magnus series.

enumerator Euler

A kick-drift integrator. Updates the momentum with an instantaneous torque-impulse, and then undergoes varying degrees of torque free precession (depending on the Order of the Magnus() series)

enumerator Leapfrog

A drift-kick-drift integrator, distinct from the Euler in that the torque is evaluated directly in the middle of a timestep, making the integrator time-reversible.