Riemannian Acceleration in Oblate Spheroidal Coordinate System  

作　　者：N. E. J. Omaghali S. X. K. Howusu N. E. J. Omaghali;S. X. K. Howusu(Department of Physics, University of Jos, Jos, Nigeria;Theoretical Physics Program, National Mathematical Centre, Abuja, Nigeria)

机构地区：[1]Department of Physics, University of Jos, Jos, Nigeria [2]Theoretical Physics Program, National Mathematical Centre, Abuja, Nigeria

出　　处：《Journal of Applied Mathematics and Physics》2016年第2期279-285,共7页应用数学与应用物理（英文）

摘　　要：The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate and realistic description of motion in these bodies can be realized. In this paper, we derive the Riemannian acceleration for motion in oblate spheroidal coordinate system using the golden metric tensor in oblate spheroidal coordinates. The Riemannian acceleration in the oblate spheroidal coordinate system reduces to the pure Newtonian acceleration in the limit of c⁰ and contains post-Newtonian correction terms of all orders of c^-2. The result obtained thereby opens the way for further studies and applications of the motion of particles in oblate spheroidal coordinate system.The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate and realistic description of motion in these bodies can be realized. In this paper, we derive the Riemannian acceleration for motion in oblate spheroidal coordinate system using the golden metric tensor in oblate spheroidal coordinates. The Riemannian acceleration in the oblate spheroidal coordinate system reduces to the pure Newtonian acceleration in the limit of c⁰ and contains post-Newtonian correction terms of all orders of c^-2. The result obtained thereby opens the way for further studies and applications of the motion of particles in oblate spheroidal coordinate system.

关 键 词：Riemannian Acceleration Golden Metric Tensor Oblate Spheroidal Coordinates Christoffel’s Symbols 

分 类 号：O18[理学—数学]