User:Tohline/Appendix/Ramblings/Bordeaux
Université de Bordeaux
|
|---|
| | Tiled Menu | Tables of Content | Banner Video | Tohline Home Page | |
Spheroid-Ring Systems
Through a research collaboration at the Université de Bordeaux, B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509 have published a paper titled, Rigidly Rotating, Incompressible Spheroid-Ring Systems: New Bifurcations, Critical Rotations, and Degenerate States.
Exterior Gravitational Potential of Toroids
J. -M. Huré, B. Basillais, V. Karas, A. Trova, & O. Semerák (2020), MNRAS, 494, 5825-5838 have published a paper titled, The Exterior Gravitational Potential of Toroids. Here we examine how their work relates to the published work by C.-Y. Wong (1973, Annals of Physics, 77, 279), which we have separately discussed in detail.
On an initial reading, it appears as though the most relevant section of the Huré, et al. (2020) paper is §8 titled, The Solid Torus. They state that the gravitational potential outside of an homogeneous (circular cross-section) torus with (major, minor) radii (RC, b) is,
|
<math>~\Psi_\mathrm{grav}(\vec{r})</math> |
<math>~=</math> |
<math>~ -4G\rho_0 \int_0^b \int_0^{2\pi} a\kappa b' d\theta db' \, , </math> |
Huré, et al. (2020), §8, p. 5831, Eq. (48)
where, the function,
<math>~\kappa \equiv \frac{K(k)}{\Delta} \, ,</math>
can be replaced by its Taylor expansion, namely …
|
<math>~</math> |
<math>~=</math> |
<math>~</math> |
|
|
|---|
|
© 2014 - 2021 by Joel E. Tohline |