This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under ...This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.展开更多
The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Ni...The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.展开更多
Purpose-The purpose of this paper is to propose radiating system by avoiding electromagnetic interference in unwanted directions and to radiate the energy in the required direction with an optimization technique.Desig...Purpose-The purpose of this paper is to propose radiating system by avoiding electromagnetic interference in unwanted directions and to radiate the energy in the required direction with an optimization technique.Design/methodology/approach-Practically,multiple,incompatible variables require concurrent boost on a synthesis of systematic antenna assemblage.The authors have worked out the main statistic penalty function to ensure all the restrictions.Here,MBPSO(Modified Binary Particle Swarm Optimization)is developed and introduced thin planar synthesis restriction.The sigmoid function is used to update the particle position.Different analytical demonstrations have been carried out,and the exhibited methods are predominant than the algorithms.Findings-A 20310 planar antenna array is synthesized using modified BPSO.The authors have suppressed the PSLL in two principal planes and as well as in the entire f plane.Numerical results state that MBPSO outperforms the other binary BPSO,BCSO,ACO,RGA,GAoptimization techniques.MBPSO achieved a51.84 dB PSLL level,whereas BPSO achieved48.57 dB with the same 50%thinning.Originality/value-Planar array antenna formation is one of the most complex syntheses because the array gets filled with more antenna elements.The machine-like complication and implementation of such an antenna arrangement with a broad opening would be expensive.It is not easy to control the required radiation patterns shape by using a uniform feeding network.To get better flexibility for sustaining the sidelobe levelheaded along with consistent amplitude distribution.So as far as prominence has been given to the evolutionary algorithm,find an ideal solution for objective array combinational problems.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10772025)the Fund for Fundamental Research of Beijing Institute of Technology
文摘This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.
文摘The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.
文摘Purpose-The purpose of this paper is to propose radiating system by avoiding electromagnetic interference in unwanted directions and to radiate the energy in the required direction with an optimization technique.Design/methodology/approach-Practically,multiple,incompatible variables require concurrent boost on a synthesis of systematic antenna assemblage.The authors have worked out the main statistic penalty function to ensure all the restrictions.Here,MBPSO(Modified Binary Particle Swarm Optimization)is developed and introduced thin planar synthesis restriction.The sigmoid function is used to update the particle position.Different analytical demonstrations have been carried out,and the exhibited methods are predominant than the algorithms.Findings-A 20310 planar antenna array is synthesized using modified BPSO.The authors have suppressed the PSLL in two principal planes and as well as in the entire f plane.Numerical results state that MBPSO outperforms the other binary BPSO,BCSO,ACO,RGA,GAoptimization techniques.MBPSO achieved a51.84 dB PSLL level,whereas BPSO achieved48.57 dB with the same 50%thinning.Originality/value-Planar array antenna formation is one of the most complex syntheses because the array gets filled with more antenna elements.The machine-like complication and implementation of such an antenna arrangement with a broad opening would be expensive.It is not easy to control the required radiation patterns shape by using a uniform feeding network.To get better flexibility for sustaining the sidelobe levelheaded along with consistent amplitude distribution.So as far as prominence has been given to the evolutionary algorithm,find an ideal solution for objective array combinational problems.
