Existence of invariant curves for a Fermi-type impact absorber

被引：3
作者：
Cao, Zhenbang [1 ]
Zhang, Xiaoming [1 ]
Li, Denghui [2 ]
Yin, Shan [3 ]
Xie, Jianhua [1 ]
机构：
[1] Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu 610031, Peoples R China
[2] Hexi Univ, Sch Math & Stat, Zhangye 734000, Peoples R China
[3] Hunan Univ, State Key Lab Adv Design & Manufacture Vehicle Bo, Changsha 410082, Hunan, Peoples R China
来源：
NONLINEAR DYNAMICS | 2020年 / 99卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Impact absorber; Moser's twist theorem; Invariant curves; Symmetry; BOUNCING BALLS; TORI;
D O I：
10.1007/s11071-019-05437-0
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper we study an impact absorber which is similar to the Fermi accelerator and can be described as a ball moves in a periodically oscillating ring with a wall and reflects elastically from the wall. First, Poincare map of the system is established. The existence of invariant curves for the map is proved based on Moser's twist theorem. Accordingly, the velocities of the ball are always bounded for any initial motion for all time. Moreover, the symmetry of the Poincare map is discussed. Finally, some numerical simulations are given to demonstrate the theoretical results.
引用
收藏
页码：2647 / 2656
页数：10
相关论文
共 27 条
[1]  
[Anonymous], 1983, Asterisque
[2]  
Arnol'd V.I., 2013, Mathematical Methods of Classical Mechanics
[3]  
Arnold VI, 1963, RUSS MATH SURV+, V18, P9, DOI DOI 10.1070/RM1963V018N05ABEH004130
[4]   Fermi acceleration on the annular billiard [J].
Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociěncias e Ciěncias Exatas, UNESP, Avenida 24A, 1515-Bela Vista, 13506-700, Rio Claro, Sao Paulo, Brazil .
Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 2006, 6
[5]   Bouncing balls in non-linear potentials [J].
Dolgopyat, Dmitry .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2008, 22 (1-2) :165-182
[6]  
Douady R, 1982, THESIS
[7]  
Fermi E., 1949, Phys. Rev., V75, P1169, DOI 10.1103/PhysRev.75.1169
[8]   Fermi acceleration in non-autonomous billiards [J].
Gelfreich, V. ;
Turaev, D. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (21)
[9]  
HERMAN MR, 1983, ASTERISQUE, P1
[10]  
Kolmogorov A. N., 1954, DOKL AKAD NAUK SSSR, V98, P527, DOI DOI 10.1007/BFB0021737
123