A numerical study of capsizing: Comparing control set analysis and Melnikov's method

被引：7

作者：

Colonius, Fritz ^{[1
]}

Marquardt, Albert ^{[1
]}

Kreuzer, Edwin ^{[2
]}

Sichermann, Wolfgang ^{[2
]}

机构：

[1] Univ Augsburg, Inst Math, D-86135 Augsburg, Germany

[2] Tech Univ Hamburg, Inst Mech & Meerestech, D-21071 Hamburg, Germany

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2008年 / 18卷 / 05期

关键词：

control sets; Melnikov method; ship roll motion;

D O I：

10.1142/S0218127408021129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two models for ship roll motion and capsizing under stochastic excitation are analyzed using Melnikov's method and control set analysis. The predictions given by these two methods are compared.

引用

页码：1503 / 1514

页数：12

共 20 条

[1] CHAOTIC TRANSPORT IN THE HOMOCLINIC AND HETEROCLINIC TANGLE REGIONS OF QUASI-PERIODICALLY FORCED 2-DIMENSIONAL DYNAMIC-SYSTEMS [J].

BEIGIE, D ;

LEONARD, A ;

WIGGINS, S .

NONLINEARITY, 1991, 4 (03) :775-819

[2] Stochastic models with multistability and extinction levels [J].

Colonius, F ;

delaRubia, F ;

Kliemann, W .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1996, 56 (03) :919-945

[3] Topological, smooth, and control techniques for perturbed systems [J].

Colonius, F ;

Kliemann, W .

STOCHASTIC DYNAMICS, 1999, :181-208

[4]

Colonius F., 2000, SYS CON FDN

[5] Near invariance for Markov diffusion systems [J].

Colonius, Fritz ;

Gayer, Tobias ;

Kliemann, Wolfgang .

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2008, 7 (01) :79-107

[6] A subdivision algorithm for the computation of unstable manifolds and global attractors [J].

Dellnitz, M ;

Hohmann, A .

NUMERISCHE MATHEMATIK, 1997, 75 (03) :293-317

[7]

Dellnitz M, 2001, ERGODIC THEORY, ANALYSIS, AND EFFICIENT SIMULATION OF DYNAMICAL SYSTEMS, P145

[8]

Dellnitz M., 2002, HDB DYNAMICAL SYSTEM, P221, DOI DOI 10.1016/S1874-575X(02)80026-1

[9] APPLICATION OF GLOBAL METHODS FOR ANALYZING DYNAMICAL SYSTEMS TO SHIP ROLLING MOTION AND CAPSIZING [J].

Falzarano, Jeffrey M. ;

Shaw, Steven W. ;

Troesch, Armin W. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1992, 2 (01) :101-115

[10] Controllability and invariance properties of time-periodic systems [J].

Gayer, T .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2005, 15 (04) :1361-1375

← 1 2 →