This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of...This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.展开更多
According to “Evolution Encyclopedia” (The Origin of the Solar System), “There is no possible means by which the angular momentum from the sun could be transferred to the planets”. Yet this is what would have to b...According to “Evolution Encyclopedia” (The Origin of the Solar System), “There is no possible means by which the angular momentum from the sun could be transferred to the planets”. Yet this is what would have to be done if any of the evolutionary theories of solar system origin are to be accepted. Scientists cannot account for this puzzling situation: less than one percent of the mass of the solar system is in the planets, while a staggering 98 percent of its angular momentum is in them. It simply does not fit into any of the cosmologies. Speaking of the mass-angular momentum problem, D. Bergamini says: “A theory of evolution that fails to account for this peculiar fact is ruled out before it starts” [1]. Angular Momentum problem is one of the most critical problems in Standard model that must be solved. To the best of our knowledge, the developed Hypersphere World-Universe Model (WUM) is only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum [2]. In the present paper, we discuss Angular Momenta of Solar System, Milky Way galaxy, and Superclusters in frames of WUM.展开更多
Measuring the orbital angular momentum(OAM)of vortex beams,including the magnitude and the sign,has great application prospects due to its theoretically unbounded and orthogonal modes.Here,the sign-distinguishable OAM...Measuring the orbital angular momentum(OAM)of vortex beams,including the magnitude and the sign,has great application prospects due to its theoretically unbounded and orthogonal modes.Here,the sign-distinguishable OAM measurement in optomechanics is proposed,which is achieved by monitoring the shift of the transmission spectrum of the probe field in a double Laguerre-Gaussian(LG)rotational-cavity system.Compared with the traditional single LG rotational cavity,an asymmetric optomechanically induced transparency window can occur in our system.Meanwhile,the position of the resonance valley has a strong correlation with the magnitude and sign of OAM.This originally comes from the fact that the effective detuning of the cavity mode from the driving field can vary with the magnitude and sign of OAM,which causes the spectral shift to be directional for different signs of OAM.Our scheme solves the shortcoming of the inability to distinguish the sign of OAM in optomechanics,and works well for high-order vortex beams with topological charge value±45,which is a significant improvement for measuring OAM based on the cavity optomechanical system.展开更多
The high rolling speed of a missile heavily affects the stabilizing capability of the inertial platform in the laser tracking system （LTS） of the missile. In this paper, a rotational stabilizing platform （RSP） and...The high rolling speed of a missile heavily affects the stabilizing capability of the inertial platform in the laser tracking system （LTS） of the missile. In this paper, a rotational stabilizing platform （RSP） and a fuzzy-PID controller is designed to stabilize the inertial platform. This controller integrates the advantages of both fuzzy controller and classic PID controller. A comparison study is carried out to illustrate the advantages of the proposed fuzzy-PID controller over the classic PID controller. Numerical results indicate that the fuzzy-PID controller outperforms the classic one in effectively handling nonlinear disturbances and quickly stabilizing the inertial platform at the sudden change of missile roiling speed.展开更多
CRTS-II slab ballastless track on bridge is a unique system in China high speed railway.The application of longitudinal continuous track system has obviously changed dynamic characteristics of bridge structure.The bri...CRTS-II slab ballastless track on bridge is a unique system in China high speed railway.The application of longitudinal continuous track system has obviously changed dynamic characteristics of bridge structure.The bridge system and CRTS-II track system form a complex nonlinear system.To investigate the seismic response of high speed railway(HSR)simply supported bridge-track system,nonlinear models of three-span simply supported bridge with piers of different height and CRTS-II slab ballastless track system are established.By seismic analysis,it is found that shear alveolar in CRTS-II track system is more prone to be damaged than bridge components,such as piers,girders and bearings.The result shows that the inconsistent displacement of bridge girders is the main cause of the CRTS-II track system’s damage.Then the rotational friction damper(RFD)is adopted,which utilizes the device’s rotation and friction to dissipate seismic energy.The hysteretic behavior of RFD is studied by numerical and experimental methods.Results prove that RFD can provide good hysteretic energy dissipation ability with stable performance.Furthermore,the analysis of RFD’s influence on seismic response of HSR bridge-track system shows that RFD with larger sliding force is more effective in controlling excessive inconsistent displacement where RFD is installed,though response of other bridge spans could slightly deteriorated.展开更多
In the 21st century, people have come to the era of ocean science and ocean economy. With the development of ocean science and technology and the thorough research on the ocean, underwater mating technique has been wi...In the 21st century, people have come to the era of ocean science and ocean economy. With the development of ocean science and technology and the thorough research on the ocean, underwater mating technique has been widely used in such fields as sunk ship salvage, deep ocean workstation, submarine lifesaving aid and military affairs. In this paper, researches are made home and abroad on mating technology. Two-joint mating system of underwater vehicle is designed including plane system, three-dimensional assembly system and control system in order to increase the capacity of adapting platform obliquity and adopting rotational skirt scheme. It is clear that the system fits the working space of underwater vehicle passageway and there is no interference phenomenon in assembly design. The finite element model of the system shell and the pressurization of the joint are established. The results of the finite element computing and the pressing test are accordant, and thus it can testify that the shell material meet the need of intension and joint pressurization is reliable. Modeling of the control system is accomplished, and simulation and analysis are made, which can provide directions for the controller design of mating system of underwater vehicles.展开更多
Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativisti...Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D'Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.展开更多
基金funded by the Deanship of Scientific Research,Princess Nourah bint Abdulrahman University,through the Program of Research Project Funding After Publication,grant No(44-PRFA-P-107).
文摘This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.
文摘According to “Evolution Encyclopedia” (The Origin of the Solar System), “There is no possible means by which the angular momentum from the sun could be transferred to the planets”. Yet this is what would have to be done if any of the evolutionary theories of solar system origin are to be accepted. Scientists cannot account for this puzzling situation: less than one percent of the mass of the solar system is in the planets, while a staggering 98 percent of its angular momentum is in them. It simply does not fit into any of the cosmologies. Speaking of the mass-angular momentum problem, D. Bergamini says: “A theory of evolution that fails to account for this peculiar fact is ruled out before it starts” [1]. Angular Momentum problem is one of the most critical problems in Standard model that must be solved. To the best of our knowledge, the developed Hypersphere World-Universe Model (WUM) is only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum [2]. In the present paper, we discuss Angular Momenta of Solar System, Milky Way galaxy, and Superclusters in frames of WUM.
基金the National Key Research and Development Program of China(Grant Nos.2017YFA0304202 and 2017YFA0205700)the National Natural Science Foundation of China(NSFC)(Grant Nos.11875231 and 11935012)the Fundamental Research Funds for the Central Universities through Grant No.2018FZA3005.
文摘Measuring the orbital angular momentum(OAM)of vortex beams,including the magnitude and the sign,has great application prospects due to its theoretically unbounded and orthogonal modes.Here,the sign-distinguishable OAM measurement in optomechanics is proposed,which is achieved by monitoring the shift of the transmission spectrum of the probe field in a double Laguerre-Gaussian(LG)rotational-cavity system.Compared with the traditional single LG rotational cavity,an asymmetric optomechanically induced transparency window can occur in our system.Meanwhile,the position of the resonance valley has a strong correlation with the magnitude and sign of OAM.This originally comes from the fact that the effective detuning of the cavity mode from the driving field can vary with the magnitude and sign of OAM,which causes the spectral shift to be directional for different signs of OAM.Our scheme solves the shortcoming of the inability to distinguish the sign of OAM in optomechanics,and works well for high-order vortex beams with topological charge value±45,which is a significant improvement for measuring OAM based on the cavity optomechanical system.
基金the China Aerospace Science and Innovation Foundation(No. 06CASC0407)
文摘The high rolling speed of a missile heavily affects the stabilizing capability of the inertial platform in the laser tracking system （LTS） of the missile. In this paper, a rotational stabilizing platform （RSP） and a fuzzy-PID controller is designed to stabilize the inertial platform. This controller integrates the advantages of both fuzzy controller and classic PID controller. A comparison study is carried out to illustrate the advantages of the proposed fuzzy-PID controller over the classic PID controller. Numerical results indicate that the fuzzy-PID controller outperforms the classic one in effectively handling nonlinear disturbances and quickly stabilizing the inertial platform at the sudden change of missile roiling speed.
基金The authors are grateful for the financial support from the Fundamental Research Funds for the Central Universities of Central South University(Project No.502221804)the National Natural Science Foundation of China(Project Nos.51878674,51878563)+1 种基金the Foundation for Key Youth Scholars in Hunan Province(Project No.150220077)the Project of Yuying Plan in Central South University(Project No.502034002).Any opinions,findings,and conclusions or recommendations expressed in this paper are those of the authors.
文摘CRTS-II slab ballastless track on bridge is a unique system in China high speed railway.The application of longitudinal continuous track system has obviously changed dynamic characteristics of bridge structure.The bridge system and CRTS-II track system form a complex nonlinear system.To investigate the seismic response of high speed railway(HSR)simply supported bridge-track system,nonlinear models of three-span simply supported bridge with piers of different height and CRTS-II slab ballastless track system are established.By seismic analysis,it is found that shear alveolar in CRTS-II track system is more prone to be damaged than bridge components,such as piers,girders and bearings.The result shows that the inconsistent displacement of bridge girders is the main cause of the CRTS-II track system’s damage.Then the rotational friction damper(RFD)is adopted,which utilizes the device’s rotation and friction to dissipate seismic energy.The hysteretic behavior of RFD is studied by numerical and experimental methods.Results prove that RFD can provide good hysteretic energy dissipation ability with stable performance.Furthermore,the analysis of RFD’s influence on seismic response of HSR bridge-track system shows that RFD with larger sliding force is more effective in controlling excessive inconsistent displacement where RFD is installed,though response of other bridge spans could slightly deteriorated.
基金supported by the Heilongjiang Provincial Natural Science Foundation (Grant No. E091002)the Postdoctoral Science-Research Developmental Foundation of Heilongjiang province (Grant No. 323630299)
文摘In the 21st century, people have come to the era of ocean science and ocean economy. With the development of ocean science and technology and the thorough research on the ocean, underwater mating technique has been widely used in such fields as sunk ship salvage, deep ocean workstation, submarine lifesaving aid and military affairs. In this paper, researches are made home and abroad on mating technology. Two-joint mating system of underwater vehicle is designed including plane system, three-dimensional assembly system and control system in order to increase the capacity of adapting platform obliquity and adopting rotational skirt scheme. It is clear that the system fits the working space of underwater vehicle passageway and there is no interference phenomenon in assembly design. The finite element model of the system shell and the pressurization of the joint are established. The results of the finite element computing and the pressing test are accordant, and thus it can testify that the shell material meet the need of intension and joint pressurization is reliable. Modeling of the control system is accomplished, and simulation and analysis are made, which can provide directions for the controller design of mating system of underwater vehicles.
基金The project supported by National Natural Science Foundation of China under Grant No. 19972010, and Natural Science Foundation of Henan Province under Grant Nos. 984053100 and 998040080
文摘Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D'Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.
