Subharmonic resonances of the parametrically driven pendulum

被引:33
作者
Butikov, EI [1 ]
机构
[1] St Petersburg State Univ, St Petersburg, Russia
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2002年 / 35卷 / 30期
关键词
D O I
10.1088/0305-4470/35/30/301
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries of these modes in the parameter space are determined. New related modes of regular behaviour are described and explained. The conditions of the inverted pendulum stability are determined with greater precision than previous results. A computer program simulating the physical system supports the analytical investigation.
引用
收藏
页码:6209 / 6231
页数:23
相关论文
共 23 条
[1]   MULTIPLE-NODDING OSCILLATIONS OF A DRIVEN INVERTED PENDULUM [J].
ACHESON, DJ .
PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1995, 448 (1932) :89-95
[2]  
[Anonymous], 1988, MECHANICS
[3]  
[Anonymous], MECHANICS
[4]   The "not quite" inverted pendulum [J].
Bishop, SR ;
Sudor, DJ .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1999, 9 (01) :273-285
[5]   STABILITY AND HOPF BIFURCATIONS IN AN INVERTED PENDULUM [J].
BLACKBURN, JA ;
SMITH, HJT ;
GRONBECHJENSEN, N .
AMERICAN JOURNAL OF PHYSICS, 1992, 60 (10) :903-908
[6]  
Butikov E. I., 1999, European Journal of Physics, V20, P429, DOI 10.1088/0143-0807/20/6/308
[7]   On the dynamic stabilization of an inverted pendulum [J].
Butikov, EI .
AMERICAN JOURNAL OF PHYSICS, 2001, 69 (07) :755-768
[8]  
BUTIKOV EI, 2002, PARAMETRICALLY DRIVE
[9]   Inverted oscillations of a driven pendulum [J].
Clifford, MJ ;
Bishop, SR .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1998, 454 (1979) :2811-2817
[10]   Experimental investigation of the "effective potential" of an inverted pendulum [J].
Fenn, JG ;
Bayne, DA ;
Sinclair, BD .
AMERICAN JOURNAL OF PHYSICS, 1998, 66 (11) :981-984