STABILITY AND HOPF BIFURCATIONS IN AN INVERTED PENDULUM

被引：90

作者：

BLACKBURN, JA

SMITH, HJT

GRONBECHJENSEN, N

机构：

[1] UNIV WATERLOO,DEPT PHYS,WATERLOO N2L 3G1,ONTARIO,CANADA

[2] TECH UNIV DENMARK,PHYS LAB 1,DK-2800 LYNGBY,DENMARK

来源：

AMERICAN JOURNAL OF PHYSICS | 1992年 / 60卷 / 10期

关键词：

D O I：

10.1119/1.17011

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

The inverted state of a simple pendulum is a configuration of unstable equilibrium. This instability may be removed if the pivot is harmonically displaced up and down with appropriate frequency and amplitude. Numerical simulations are employed to investigate the stable domains of the system. The associated basins of attraction, extracted by interpolated cell mapping, are seen to be fractal. Loss of stability at high excitation amplitudes is observed to follow a Hopf bifurcation.

引用

页码：903 / 908

页数：6

共 20 条

[1]

BAKER GL, 1990, CHAOTIC DYNAMICS

[2] DRIVEN PENDULUM FOR STUDYING CHAOS [J].

BLACKBURN, JA ;

VIK, S ;

WU, BR ;

SMITH, HJT .

REVIEW OF SCIENTIFIC INSTRUMENTS, 1989, 60 (03) :422-426

[3]

Corben H.C., 1960, CLASSICAL MECH, P67

[4] THE INVERTED PENDULUM - A MECHANICAL ANALOG OF THE QUADRUPOLE MASS FILTER [J].

FRIEDMAN, MH ;

CAMPANA, JE ;

KELNER, L ;

SEELIGER, EH ;

YERGEY, AL .

AMERICAN JOURNAL OF PHYSICS, 1982, 50 (10) :924-931

[5]

HAYASHI C, 1985, NONLINEAR OSCILLATIO, P86

[6]

LANDAU L. D., 1976, MECHANICS, P93

[7]

LEVEN RW, 1985, PHYSICA D, V16, P371, DOI 10.1016/0167-2789(85)90015-6

[8] STUDY OF THE DRIVEN DAMPED PENDULUM - APPLICATION TO JOSEPHSON-JUNCTIONS AND CHARGE-DENSITY-WAVE SYSTEMS [J].

MACDONALD, AH ;

PLISCHKE, M .

PHYSICAL REVIEW B, 1983, 27 (01) :201-211

[9]

Marsden J.E., 2012, HOPF BIFURCATION ITS, V19

[10]

MCLACHAN NW, 1951, THEORY APPL MATHIEU, P39

← 1 2 →