# Center of inertia and coordinate transformations in the post-Newtonian charged n-body problem in gravitation

## Document Type

Article

## Publication Date

1-1-1978

## Abstract

We generalize the field theory propagator by finding a way to make it a function of some additional arbitrary parameters. Thus, it is now possible to obtain Lagrangians (which contain the propagator parameters) from field theory in a more general coordinate system than had previously been possible. We find the n-body (classical) Bazański Lagrangian in this more general coordinate system and we give the relationship between the various coordinate systems by an n-body coordinate transformation involving the propagator parameters. We find the center of inertia for the case of the n-body Basz·ański Lagrangian in the general coordinate system and find that the potential energy terms -Gmimj/rij and eiej/rij do not in general split equally between particles i and j as they do in the case of Baz·ański coordinates. We also find the center of inertia for the case of the n-body (unchanged) post-Newtonian Lagrangian with parameterized post-Newtonian (PPN) parameters γ and β in standard coordinates, and show that the potential energy terms do split equally between a pair of particles. © 1979 American Institute of Physics.

## Publication Source (Journal or Book title)

Journal of Mathematical Physics

## First Page

1427

## Last Page

1434

## Recommended Citation

Barker, B., & O'Connell, R.
(1978). Center of inertia and coordinate transformations in the post-Newtonian charged n-body problem in gravitation.* Journal of Mathematical Physics**, 20* (7), 1427-1434.
https://doi.org/10.1063/1.524225