We calculate the canonical angular momentum of a free electron, positron and gamma photon. We show that for any particle with charge q the canonical angular momentum (J<sub>c</sub>) is written as the summa...We calculate the canonical angular momentum of a free electron, positron and gamma photon. We show that for any particle with charge q the canonical angular momentum (J<sub>c</sub>) is written as the summation of the kinetic angular momentum (J<sub>kin</sub>) and the intrinsic quantum flux dependent terms. In terms of the z-components this can be written as . For a free electron (e<sup>-</sup>) and a positron (e<sup>+</sup>) depending on the spin orientation we find that:;;and respectively. Similarly for a gamma (γ) photon, propagating in z direction with an angular frequency ω, the canonical angular momentum is found to be: , here the (+) and (-) signs stand for the right and left hand circular helicity respectively.展开更多
We had previously obtained analytical formulae for the dipole moments and angular momenta of rotating spherical bodies. The resulting formulae were applied to the Sun, the star 78 Virginis and the Earth. The agreement...We had previously obtained analytical formulae for the dipole moments and angular momenta of rotating spherical bodies. The resulting formulae were applied to the Sun, the star 78 Virginis and the Earth. The agreement of the theoretical formulae with the actual real situations is indeed remarkable. In this note we apply the same formulae to the electron and the proton, using the classical values of the radii, so no quantum mechanical treatment is considered.展开更多
The dipole moments, angular momenta and gyromagnetic ratios of the electron and the proton were obtained earlier. In this note, we derive the corresponding expressions for the neutron and the muon. This work relies on...The dipole moments, angular momenta and gyromagnetic ratios of the electron and the proton were obtained earlier. In this note, we derive the corresponding expressions for the neutron and the muon. This work relies on the results obtained earlier for the angular momenta and dipole moments of rotating spherical bodies.展开更多
From the wave equation of a generalized beam the orbital angular momentum is studied. It is shown that the orbital angular momentum exists not only in the Laguerre-Gaussian beam, but in any beam with an angular-depend...From the wave equation of a generalized beam the orbital angular momentum is studied. It is shown that the orbital angular momentum exists not only in the Laguerre-Gaussian beam, but in any beam with an angular-dependent structure. By calculating the second order intensity moments of the beam the relation between the orbital angular momentum and the second order moments 〈xθy〉, 〈yθx〉 is given. As an example the orbital angular momentum of the general astigmatic Gaussian beam is studied.展开更多
Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dy...Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.展开更多
This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular ...This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.展开更多
Based on Fourier transform,the angular spectrum equation and its discrete model of the inverse source problem of the two-dimensional Helmholtz equation are derived.By transforming the two-dimensional inverse source pr...Based on Fourier transform,the angular spectrum equation and its discrete model of the inverse source problem of the two-dimensional Helmholtz equation are derived.By transforming the two-dimensional inverse source problem in the spatial domain into the inverse source problem in the one-dimensional Fourier domain,the source intensity angular spectrum vector in the Fourier domain is calculated by the one-dimensional method of moments.Then,using the discrete Fourier inverse transform,a multi-frequency angular spectrum method of moments is proposed to reconstruct the inverse source problem of the two-dimensional Helmholtz equation.The reconstruction accuracy and stability of this method are improved by optimizing the excitation wavenumber sequence.Simulation calculations show that the multi-frequency angular spectrum method of moments has high reconstruction accuracy and anti-noise ability,and can also design the reconstruction model according to the effective frequency band of the acoustic sensor to achieve the highest resolution.In addition,since the calculation of the coefficient matrix of the proposed method is independent of the distribution of the source intensity function and does not require regularization processing,when the size and resolution of the required source intensity distribution area are determined,after the coefficient matrix is calculated and saved,the source intensity function corresponding to the region of interest can be reconstructed according to different sound pressure detection data,with high calculation accuracy and efficiency.展开更多
We have calculated the intrinsic magnetic moment of a photon through the intrinsic magnetic moment of a gamma photon created as a result of the electron-positron annihilation with the angular frequency ω. We show tha...We have calculated the intrinsic magnetic moment of a photon through the intrinsic magnetic moment of a gamma photon created as a result of the electron-positron annihilation with the angular frequency ω. We show that a photon propagating in z direction with an angular frequency ω carries a magnetic moment of μz = ±(ec/ω) along the propagation direction. Here, the (+) and (-) signs stand for the right hand and left circular helicity respectively. Because of these two symmetric values of the magnetic moment, we expect a splitting of the photon beam into two symmetric subbeams in a Stern-Gerlach experiment. The splitting is expected to be more prominent for low energy photons. We believe that the present result will be helpful for understanding the recent attempts on the Stern-Gerlach experiment with slow light and the behavior of the dark polaritons and also the atomic spinor polaritons.展开更多
The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the gene...The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.展开更多
文摘We calculate the canonical angular momentum of a free electron, positron and gamma photon. We show that for any particle with charge q the canonical angular momentum (J<sub>c</sub>) is written as the summation of the kinetic angular momentum (J<sub>kin</sub>) and the intrinsic quantum flux dependent terms. In terms of the z-components this can be written as . For a free electron (e<sup>-</sup>) and a positron (e<sup>+</sup>) depending on the spin orientation we find that:;;and respectively. Similarly for a gamma (γ) photon, propagating in z direction with an angular frequency ω, the canonical angular momentum is found to be: , here the (+) and (-) signs stand for the right and left hand circular helicity respectively.
文摘We had previously obtained analytical formulae for the dipole moments and angular momenta of rotating spherical bodies. The resulting formulae were applied to the Sun, the star 78 Virginis and the Earth. The agreement of the theoretical formulae with the actual real situations is indeed remarkable. In this note we apply the same formulae to the electron and the proton, using the classical values of the radii, so no quantum mechanical treatment is considered.
文摘The dipole moments, angular momenta and gyromagnetic ratios of the electron and the proton were obtained earlier. In this note, we derive the corresponding expressions for the neutron and the muon. This work relies on the results obtained earlier for the angular momenta and dipole moments of rotating spherical bodies.
文摘From the wave equation of a generalized beam the orbital angular momentum is studied. It is shown that the orbital angular momentum exists not only in the Laguerre-Gaussian beam, but in any beam with an angular-dependent structure. By calculating the second order intensity moments of the beam the relation between the orbital angular momentum and the second order moments 〈xθy〉, 〈yθx〉 is given. As an example the orbital angular momentum of the general astigmatic Gaussian beam is studied.
文摘Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.
文摘This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.
基金supported by the National Natural Science Foundation of China(51775121,12364055).
文摘Based on Fourier transform,the angular spectrum equation and its discrete model of the inverse source problem of the two-dimensional Helmholtz equation are derived.By transforming the two-dimensional inverse source problem in the spatial domain into the inverse source problem in the one-dimensional Fourier domain,the source intensity angular spectrum vector in the Fourier domain is calculated by the one-dimensional method of moments.Then,using the discrete Fourier inverse transform,a multi-frequency angular spectrum method of moments is proposed to reconstruct the inverse source problem of the two-dimensional Helmholtz equation.The reconstruction accuracy and stability of this method are improved by optimizing the excitation wavenumber sequence.Simulation calculations show that the multi-frequency angular spectrum method of moments has high reconstruction accuracy and anti-noise ability,and can also design the reconstruction model according to the effective frequency band of the acoustic sensor to achieve the highest resolution.In addition,since the calculation of the coefficient matrix of the proposed method is independent of the distribution of the source intensity function and does not require regularization processing,when the size and resolution of the required source intensity distribution area are determined,after the coefficient matrix is calculated and saved,the source intensity function corresponding to the region of interest can be reconstructed according to different sound pressure detection data,with high calculation accuracy and efficiency.
文摘We have calculated the intrinsic magnetic moment of a photon through the intrinsic magnetic moment of a gamma photon created as a result of the electron-positron annihilation with the angular frequency ω. We show that a photon propagating in z direction with an angular frequency ω carries a magnetic moment of μz = ±(ec/ω) along the propagation direction. Here, the (+) and (-) signs stand for the right hand and left circular helicity respectively. Because of these two symmetric values of the magnetic moment, we expect a splitting of the photon beam into two symmetric subbeams in a Stern-Gerlach experiment. The splitting is expected to be more prominent for low energy photons. We believe that the present result will be helpful for understanding the recent attempts on the Stern-Gerlach experiment with slow light and the behavior of the dark polaritons and also the atomic spinor polaritons.
文摘The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.
