• Corpus ID: 67778131

Exact gravitational potential of a homogeneous torus in toroidal coordinates and a surface integral approach to Poisson's equation

@article{Maji2018ExactGP,
  title={Exact gravitational potential of a homogeneous torus in toroidal coordinates and a surface integral approach to Poisson's equation},
  author={Matt Maji{\'c}},
  journal={arXiv: Classical Physics},
  year={2018}
}
  • Matt Majić
  • Published 27 February 2018
  • Mathematics, Physics
  • arXiv: Classical Physics
New exact solutions are derived for the gravitational potential inside and outside a homogeneous torus as rapidly converging series of toroidal harmonics. The approach consists of splitting the inter- nal potential into a known solution to Poisson's equation plus some solution to Laplace's equation. The full solutions are then obtained using two equivalent methods, applying differential boundary conditions at the surface, or evaluating a surface integral derived from Green's third identity… 

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