Exact and Approximate Values of the Period for a “Truly Nonlinear” Oscillator: x + x + x^(1/3)= 0  

作　　者：Ronald E.Mickens Dorian Wilkerson 

机构地区：[1]Department of Physics,Clark Atlanta University,Atlanta,GA 30314,USA [2]Department of Mathematics,Clark Atlanta University,Atlanta,GA 30314,USA

出　　处：《Advances in Applied Mathematics and Mechanics》2009年第3期383-390,共8页应用数学与力学进展（英文）

基　　金：supported in part by CAU School of Arts and Sciences Faculty Development Funds.

摘　　要：We investigate the mathematical properties of a“truly nonlinear”oscillator differential equation.In particular,using phase-space methods,it is shown that all solutions are periodic and the fixed-point is a nonlinear center.We calculate both exact and approximate analytical expressions for the period,where the exact solution is given in terms of elliptic functions and the method of harmonic balance is used to calculate the approximate formula.

关 键 词：Nonlinear oscillations periodic solutions qualitative methods special functions 

分 类 号：O17[理学—数学]