To study the rolling motion of a ship in the presence of water on its deck,a linear-plus-quadratic damping term was incorporated into its equation of motion.Ship model tests indicates that the key dynamics of the phys...To study the rolling motion of a ship in the presence of water on its deck,a linear-plus-quadratic damping term was incorporated into its equation of motion.Ship model tests indicates that the key dynamics of the physical system are preserved in the ship rolling equation with the linear-plus-quadratic type damping term.To take into account the presence of randomness in the excitation and the response,a new method was developed and a Melnikov criterion was obtained to provide an upper bound on the domain of the potential chaotic rolling motion(erratic rocking).Additionally,the Melnikov criterion proposed in this study was verified by the utilization of phase plane diagrams and Poincare maps.Furthermore,this research has made the initial endeavor to systematically modify the system parameters in the rolling equation of motion for ship stability analysis.展开更多
The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux...The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux invariant when c=2b.Using this invariant and the Poincarécompactification technique we describe analytically its global dynamics.展开更多
文摘To study the rolling motion of a ship in the presence of water on its deck,a linear-plus-quadratic damping term was incorporated into its equation of motion.Ship model tests indicates that the key dynamics of the physical system are preserved in the ship rolling equation with the linear-plus-quadratic type damping term.To take into account the presence of randomness in the excitation and the response,a new method was developed and a Melnikov criterion was obtained to provide an upper bound on the domain of the potential chaotic rolling motion(erratic rocking).Additionally,the Melnikov criterion proposed in this study was verified by the utilization of phase plane diagrams and Poincare maps.Furthermore,this research has made the initial endeavor to systematically modify the system parameters in the rolling equation of motion for ship stability analysis.
基金supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00the H2020 European Research Council grant MSCA-RISE-2017-777911+2 种基金AGAUR(Generalitat de Catalunya)grant 2021SGR00113the Reial Acadèmia de Ciències i Arts de Barcelonasupported by FCT/Portugal through CAMGSD,IST-ID,projects UIDB/04459/2020 and UIDP/04459/2020.
文摘The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux invariant when c=2b.Using this invariant and the Poincarécompactification technique we describe analytically its global dynamics.
