Periodic orbits of mechanical systems with homogeneous polynomial terms of degree five

被引：3
|
作者：
Castro Ortega, Alberto [1 ]
机构：
[1] Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City 04510, DF, Mexico
来源：
ASTROPHYSICS AND SPACE SCIENCE | 2016年 / 361卷 / 01期
关键词：
Averaging method; Polynomial potential; Periodic solutions; CHAOS;
D O I：
10.1007/s10509-015-2612-0
中图分类号：
P1 [天文学];
学科分类号：
0704 ;
摘要：
In this work the existence of periodic solutions is studied for the Hamiltonian functions H = 1/2 (p(X)(2) + p(Y)(2) + X-2 + Y-2) + a/5 X-5 + bX(3)Y(2), where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two real parameters a and b. Using the averaging method of second order we provide the sufficient conditions on the parameters to guarantee the existence of periodic solutions for positive energy and we study the stability of these periodic solutions.
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页码：1 / 8
页数：8
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