centre_of_mass_frame.hpp File Reference

Moving a sampled configuration into its own centre-of-mass frame. More...

#include "orrery/core/particle_data.hpp"

Go to the source code of this file.

Functions
void	orrery::initial_conditions::move_to_centre_of_mass_frame (core::ParticleData &data)
	Shift positions so the centre of mass is at the origin, and velocities so the total momentum is zero.

Detailed Description

Moving a sampled configuration into its own centre-of-mass frame.

A configuration drawn from a spherically symmetric model has a centre of mass near the origin and a net momentum near zero, but only near: both are sums of N random draws and so are of order the square root of N away from the values the model has. Left alone, that residue drifts the whole system across the volume during a long integration, and it puts a term into the angular momentum that depends on where the system happens to be rather than on how it is rotating.

It also spoils the tests. A property test asserting that total momentum is conserved to round-off is far sharper when the conserved value is zero, and an angular momentum measured about the origin only equals the one measured about the centre of mass when the two coincide.

This is a step a sampler applies to itself, not something a caller must remember; it is public because the tests check it directly and because a configuration assembled by hand from several pieces needs it too.

Function Documentation

move_to_centre_of_mass_frame()

void orrery::initial_conditions::move_to_centre_of_mass_frame

(

core::ParticleData &

data

)

Shift positions so the centre of mass is at the origin, and velocities so the total momentum is zero.

Both shifts are subtractions of one vector from every particle, so the internal structure of the configuration is untouched: separations, and therefore the potential energy, are exactly what they were, and relative velocities are too.

The result is not exactly centred, because the mean of the shifted values is itself a rounded sum. It is centred to round-off, which is the accuracy the conservation tests are written at.

Configurations that are exact by construction, the Kepler two-body among them, do not use this. Applying it would replace their exact zero with a rounded one.