Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure...Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure of semidirect product, and Hamiltonian is derived from Jacobi's integral. The above method can be generalized to establish the Hamiltonian structure of a rigid body with a flexible attachment in a circular or- bit. At last, an example of stability analysis is given.展开更多
The cracking of coatings and the deformation of base frustrate the application of laser cladding technology especially on surface of the ring circular orbit.In order to solve the two problems above,the stress and stra...The cracking of coatings and the deformation of base frustrate the application of laser cladding technology especially on surface of the ring circular orbit.In order to solve the two problems above,the stress and strain fields of the laser cladding process on the ring circular orbit were analyzed through the finite-element method,based on the temperature field.The wedge module of the ring circular ring was the subject investigated. The calculating results show that during the cladding process the crank point tends to generate the transversal crack;the centre point on the coating/base interface tends to generate longitudinal crack;the intersecting edge of the coating and base tends to generate toe crack.Moreover,the cracking tendency of the outer marginal point is obviously greater than that of the inner marginal point.The rather high stress appears at the border position where the constraint exists,and the stress on the point in front of molten pool under the range of laser irradiation is large as well.And the displacement becomes larger as the cladding process proceeds.展开更多
The photodetachment of a hydrogen negative ion inside a circular microcavity is studied based on the semiclassical closed orbit theory. The closed orbit of the photo-detached electron in a circular microcavity is inve...The photodetachment of a hydrogen negative ion inside a circular microcavity is studied based on the semiclassical closed orbit theory. The closed orbit of the photo-detached electron in a circular microcavity is investigated and the photodetachment cross section of this system is calculated. The calculation result suggests that oscillating structure appears in the photodetachment cross section, which is caused by the interference effects of the returning electron waves with the outgoing waves traveling along the closed orbits. Besides, our study suggests that the photodetachment cross section of the negative ions depends on the laser polarization sensitively. In order to show the correspondence between the cross section and the closed orbits of the detached electron clearly, we calculate the Fourier transformation of the cross section and find that each peak corresponds to the length of one closed orbit. We hope that our results will be useful for understanding the photodetachment process of negative ions or the electron transport in a microcavity.展开更多
We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two a...We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.展开更多
We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits per...We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits perpendicular to the incidence direction. As a main result of our calculation, we obtain in addition to the well-known alteration of the radial distance a time dependent correction term for the phase modifying the circular motion of the particle. A background of gravitational waves creates some kind of uncertainty.展开更多
We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate...We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate system.展开更多
In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild ...In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. In this article, by starting from this correct Schwarzschild metric, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Moreover, we analyse these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.展开更多
A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields a...A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.展开更多
The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbi...The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbits around L1 and L2 for the seven satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus) of Saturn in the frame work of CRTBP. It is found that the oblateness effect of Saturn on the halo orbits of the satellites closer to Saturn has significant effect compared to the satellites away from it. The halo orbits L1 and L2 are found to move towards Saturn with oblateness.展开更多
基金The projeet supported by National Natural Science Foundation of China and Aeronautic Science Foundation.
文摘Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure of semidirect product, and Hamiltonian is derived from Jacobi's integral. The above method can be generalized to establish the Hamiltonian structure of a rigid body with a flexible attachment in a circular or- bit. At last, an example of stability analysis is given.
文摘The cracking of coatings and the deformation of base frustrate the application of laser cladding technology especially on surface of the ring circular orbit.In order to solve the two problems above,the stress and strain fields of the laser cladding process on the ring circular orbit were analyzed through the finite-element method,based on the temperature field.The wedge module of the ring circular ring was the subject investigated. The calculating results show that during the cladding process the crank point tends to generate the transversal crack;the centre point on the coating/base interface tends to generate longitudinal crack;the intersecting edge of the coating and base tends to generate toe crack.Moreover,the cracking tendency of the outer marginal point is obviously greater than that of the inner marginal point.The rather high stress appears at the border position where the constraint exists,and the stress on the point in front of molten pool under the range of laser irradiation is large as well.And the displacement becomes larger as the cladding process proceeds.
基金the National Natural Science Foundation of China(Grant No.11074104)the Higher Educational Science and Technology Program of Shandong Province,China(Grant No.J13LJ04)the University Student's Science&Technology Innovation Fund of Ludong University,China(Grant No.12z004)
文摘The photodetachment of a hydrogen negative ion inside a circular microcavity is studied based on the semiclassical closed orbit theory. The closed orbit of the photo-detached electron in a circular microcavity is investigated and the photodetachment cross section of this system is calculated. The calculation result suggests that oscillating structure appears in the photodetachment cross section, which is caused by the interference effects of the returning electron waves with the outgoing waves traveling along the closed orbits. Besides, our study suggests that the photodetachment cross section of the negative ions depends on the laser polarization sensitively. In order to show the correspondence between the cross section and the closed orbits of the detached electron clearly, we calculate the Fourier transformation of the cross section and find that each peak corresponds to the length of one closed orbit. We hope that our results will be useful for understanding the photodetachment process of negative ions or the electron transport in a microcavity.
文摘We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.
文摘We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits perpendicular to the incidence direction. As a main result of our calculation, we obtain in addition to the well-known alteration of the radial distance a time dependent correction term for the phase modifying the circular motion of the particle. A background of gravitational waves creates some kind of uncertainty.
文摘We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate system.
文摘In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. In this article, by starting from this correct Schwarzschild metric, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Moreover, we analyse these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.
基金supported by the National Natural Science Foundation of China(10702003)
文摘A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.
文摘The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbits around L1 and L2 for the seven satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus) of Saturn in the frame work of CRTBP. It is found that the oblateness effect of Saturn on the halo orbits of the satellites closer to Saturn has significant effect compared to the satellites away from it. The halo orbits L1 and L2 are found to move towards Saturn with oblateness.
