This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the c...This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.展开更多
In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are dis-cussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the H...In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are dis-cussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed, the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.展开更多
This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dyn...This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton's canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether's theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.展开更多
In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is gi...In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.展开更多
Two kinds of integrals of generalized Hamilton systems with additional terms are discussed. One kind is the integral deduced by Poisson method; the other is Hojman integral obtained by Lie symmetry.
Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation ...Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.展开更多
The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetr...The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetryis studied,and Hojman adiabatic invariants of Hamilton system are obtained.An example is given to illustrate theapplication of the results.展开更多
The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of s...The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.展开更多
This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the...This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.展开更多
In this paper,we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented.The condition under which the Lie symmetry of the sy...In this paper,we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented.The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given.Meanwhile,an example is discussed to illustrate the application of the results.The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.展开更多
The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete ...The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.展开更多
A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled ...A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled holonomic Hamilton systems excited by Gaussian noise is formulated. A theory to stabilize the system is provided. Finally, one example is given to illustrate the application procedures.展开更多
The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quan...The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity,as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results.展开更多
By introducing the Hamilton theory and algorithms into the problems of laminated composite plates andshells, the Hamiltion type generalized variational principle is established, and the Hamilton canonical equations an...By introducing the Hamilton theory and algorithms into the problems of laminated composite plates andshells, the Hamiltion type generalized variational principle is established, and the Hamilton canonical equations andthe boundary conditions for the static and elastoplastic analysis of composite plates are presented. With thetransformation of phase variables, the Hamilton canonical equations and their boundary conditions for thecylindrical shells and doubly curved shells in the curvilinear coordinate are given.展开更多
By giving up any assumptions about displacement models and stress distribution,the mixed state Hamilton equation for the axisymmetric problem of the thick laminated closed cantilever cylindrical shells is established....By giving up any assumptions about displacement models and stress distribution,the mixed state Hamilton equation for the axisymmetric problem of the thick laminated closed cantilever cylindrical shells is established.An identical analytical solution is obtained for the thin,moderately thick and thick laminated closed cantilever cylindrical shells.All equations of elasticity can be satis- fied,and all elastic constants can be taken into account.展开更多
The form invariance and the Lie symmetry are defined for Hamilton systems.A relation between the form invariance and the Lie symmetry is derived.The Hojman conserved quantity is constructed by using the generators of ...The form invariance and the Lie symmetry are defined for Hamilton systems.A relation between the form invariance and the Lie symmetry is derived.The Hojman conserved quantity is constructed by using the generators of Lie symmetry.An approach to find Hojman conserved quantities in terms of the form invariance is presented.An example is given to illustrate the application of the results.展开更多
Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traver...Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10972151 and 11272227)the Innovation Program for Scientific Research in Higher Education Institution of Jiangsu Province,China(Grant No.CXLX11 0961)the Innovation Program for Scientific Research of Suzhou University of Science and Technology,China(Grant No.SKCX12S 039)
文摘In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are dis-cussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed, the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(Grant Nos.10972151 and 11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(Grant No.CXLX11_0961)
文摘This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton's canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether's theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.
文摘In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation (Grant No 10272021) and Doctoral Programme Foundation of Institute of Higher Education of China (Grant No 20040007022).
文摘Two kinds of integrals of generalized Hamilton systems with additional terms are discussed. One kind is the integral deduced by Poisson method; the other is Hojman integral obtained by Lie symmetry.
文摘Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.
文摘The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetryis studied,and Hojman adiabatic invariants of Hamilton system are obtained.An example is given to illustrate theapplication of the results.
基金Project supported by the National Aeronautics Base Science Foundation of China (No.2000CB080601)the National Defence Key Pre-research Program of China during the 10th Five-Year Plan Period (No.2002BK080602)
文摘The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.
基金supported by the National Natural Science Foundation of China (Grant Nos 10472040,10572021 and 10772025)the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005)
文摘This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.
基金Projct supported by the Natural Science Foundation of Shandong Province,China (Grant No. ZR2011AM012)the Fundamental Research Funds for the Central Universities,China (Grant No. 09CX04018A)
文摘In this paper,we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented.The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given.Meanwhile,an example is discussed to illustrate the application of the results.The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.
基金the National Natural Science Foundation of China(10272022)
文摘The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.
基金Sponsored by the National Natural Science Foundation of China (1057202110472040)Fundamental Research Foundation of Beijing Institute of Technology (BIT-UBF-200507A4206)
文摘A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled holonomic Hamilton systems excited by Gaussian noise is formulated. A theory to stabilize the system is provided. Finally, one example is given to illustrate the application procedures.
文摘The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity,as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results.
文摘By introducing the Hamilton theory and algorithms into the problems of laminated composite plates andshells, the Hamiltion type generalized variational principle is established, and the Hamilton canonical equations andthe boundary conditions for the static and elastoplastic analysis of composite plates are presented. With thetransformation of phase variables, the Hamilton canonical equations and their boundary conditions for thecylindrical shells and doubly curved shells in the curvilinear coordinate are given.
基金the National Natural Science Foundation of China
文摘By giving up any assumptions about displacement models and stress distribution,the mixed state Hamilton equation for the axisymmetric problem of the thick laminated closed cantilever cylindrical shells is established.An identical analytical solution is obtained for the thin,moderately thick and thick laminated closed cantilever cylindrical shells.All equations of elasticity can be satis- fied,and all elastic constants can be taken into account.
基金Project supported by the National Natural Science Foundation of China under Grant No.10872037the National Natural Science Foundation of Anhui Province under Grant No.070416226.
文摘The form invariance and the Lie symmetry are defined for Hamilton systems.A relation between the form invariance and the Lie symmetry is derived.The Hojman conserved quantity is constructed by using the generators of Lie symmetry.An approach to find Hojman conserved quantities in terms of the form invariance is presented.An example is given to illustrate the application of the results.
基金Project supported by the Heilongjiang Province Natural Science Foundation Joint Guidance Project,China (Grant No.LH2020F022)the Fundamental Research Funds for the Central Universities,China (Grant No.3072022CF0801)。
文摘Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.