Central Conservative Forces and Orbits beyond Conic Sections  

作　　者：Haiduke Sarafian Masataka Kaneko Setsuo Takato 

机构地区：[1]Pennsylvania State University, Commonwealth College, York, PA, USA [2]Toho University, Department of Pharmacology, Funabashi, Japan

出　　处：《Journal of Mathematics and System Science》2014年第8期579-585,共7页数学和系统科学（英文版）

摘　　要：The well-known characteristics of orbitals of classic central conservative force stems from the forces in proportion to the inverse square distance. In this article the authors extend the scope of the interest to central forces that are in proportion to algebraic integer powers of distance. Specifically, we investigate cases where the power of the distance varies between -2 to 4. Within this range the classic conic sections are associates with n = -2. The equation of motion leading to the orbitals only for n = I and -2 are analytically solvable. The remaining cases are analytically unsolvable nonlinear differential equations. Utilizing Computer Algebra System （CAS） we solve these equations numerically. For certain values of n numeric solutions are conducive to unseen trajectories.

关 键 词：曲线轨道 保守力 圆锥 中央 非线性微分方程 计算机代数系统 代数整数 功率变化 

分 类 号：O31[理学—一般力学与力学基础] U213.23[理学—力学]