For the stationary Wigner equation with inflow boundary conditions, the numerical convergence with respect to the velocity mesh size are deteriorated due to the singularity at velocity zero. In this paper, using the f...For the stationary Wigner equation with inflow boundary conditions, the numerical convergence with respect to the velocity mesh size are deteriorated due to the singularity at velocity zero. In this paper, using the fact that the solution of the stationary Wigner equation is subject to an integral constraint, we prove that the Wigner equation can be written into a form with a bounded operator B[V]. which is equivalent to the operatorA[V]=θ[V]/v in the original Wigner equation under some conditions. Then the discrete operators discretizing B[V] are proved to be uniformly bounded with respect to the mesh size. Basted on the thcoretical findings, a singularity-free numerical incthod is proposed. Numerical results are provided to show our improved numerical scheme performs much better in numerical convergence than the original scheme based on discretizing A[V].展开更多
This paper investigates the robust relative pose control for spacecraft rendezvous and docking with constrained relative pose and saturated control inputs.A barrier Lyapunov function is used to ensure the constraints ...This paper investigates the robust relative pose control for spacecraft rendezvous and docking with constrained relative pose and saturated control inputs.A barrier Lyapunov function is used to ensure the constraints of states,so that the computational singularity of the inverse matrix in control command can be avoided,while a linear auxiliary system is introduced to handle with the adverse effect of actuator saturation.The tuning rules for designing parameters in control command and auxiliary system are derived based on the stability analysis of the closed-loop system.It is proved that all closed-loop signals always keep bounded,the prescribed constraints of relative pose tracking errors are never violated,and the pose tracking errors ultimately converge to small neighborhoods of zero.Simulation experiments validate the performance of the proposed robust saturated control strategy.展开更多
The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft ro...The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft robotics,flexible electronics,and biomedicine.Theoretical investigations on large deformations of HMS structures are significant foundations of their applications.This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams.A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact(GE)beam model.The singularity-free governing equations for the three-dimensional(3D)large deformations of an HMS beam are first derived,and then solved with the Galerkin discretization method and the trustregion-dogleg iterative algorithm.The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones.The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples.It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field.The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.展开更多
A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work e...A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work explores the use of the satellite ground-track vector as the differential correction variable.The geodetic latitude is recovered by well-known elementary means.A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed.Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth’s surface,throughout the LEO-GEO range of applications.As a result,a single iteration of the continued fraction iteration yields a maximum error for the satellite height of 10??11 km.and maximum error for the geodetic anomaly of 10??9 rad.The coordinate transformation is completed by non-iteratively recovering the satellite height and the geodetic anomaly.No Taylor expansions are introduced and no Jacobian sensitivity calculations are required.For all practical applications the new algorithm provides a closed-form solution.The accuracy and algorithmic performance of the proposed approach is compared with other state of the art algorithms.展开更多
The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions...The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions. Because of the motion un- certainty at singular points, while the manipulator traverses this kind of hypersurface from one singularity-free region to another, its motion cannot be predetermined. In this paper, a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented. First, the singular point transfer disturbance and the pose disturbance, which make the perturbed singular point transfer horizontally and vertically, respectively, are constructed. Through applying these disturbances into the input parameters within the maximum loss control domain, the perturbed persistent configuration is transformed into its corresponding non-persistent one. Under the action of the disturbances, the manipulator can traverse the singularity hypersurface from one singularity-flee region to another with a desired configuration.展开更多
In this paper we will see the model of Universe according to Dynamic Universe Model of Cosmology by visualizing various processes that are happening in the Universe as per experimental evidences. For simplifying the m...In this paper we will see the model of Universe according to Dynamic Universe Model of Cosmology by visualizing various processes that are happening in the Universe as per experimental evidences. For simplifying the matter here, we will see in part 1: about the Galaxy life cycle, where the birth and death of Galaxies discussed. Probably Universe gives guidance for the movement of Galaxies. We call this Part 1: Thinking and Reproducing Universe or Mindless Universe? (Galaxy life cycle). We see every day Sun, Stars, Galaxies etc., dissipating enormous energy in the form of radiation by the way of fusion of Hydrogen to helium. So after sometime all the Hydrogen is spent and Universe will die, is it not? … Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes in frequency and finally will convert into neutrinos (mass). Hence Dynamic Universe Model proposes another process where energy will be converted back into matter and the cycle energy to mass to energy continues, sustaining the Universe to maintain this present status for ever in this form something like a Steady state model without any expansion. This we will see in Part 2: Energy - Mass - Energy Cycle. After converting energy into mass “how various elements are formed and where they are formed?” will be next logical question. Dynamic Universe Model says that these various particles change into higher massive particles or may get bombarded into stars or planets and various elements are formed. Here we bifurcate the formation of elements into 6 processes. They are for Elementary particles and elements generated in frequency changing process, By Cosmic rays, By Small stars, By Large Stars, By Super Novae and Manmade elements By Neutron Stars. This we will discuss in Part 3: Nucleosynthesis.展开更多
We propose a model with 3-dimensional spatial sections, constructed from hyperbolic cusp space glued to Seifert manifolds which are in this case homology spheres. The topological part of this research is based on Thur...We propose a model with 3-dimensional spatial sections, constructed from hyperbolic cusp space glued to Seifert manifolds which are in this case homology spheres. The topological part of this research is based on Thurston’s conjecture which states that any 3-dimensional manifold has a canonical decomposition into parts, each of which has a particular geometric structure. In our case, each part is either a Seifert fibered or a cusp hyperbolic space. In our construction we remove tubular neighbourhoods of singular orbits in areas of Seifert fibered manifolds using a splice operation and replace each with a cusp hyperbolic space. We thus achieve elimination of all singularities, which appear in the standard-like cosmological models, replacing them by “a torus to infinity”. From this construction, we propose an alternative manifold for cosmology with finite volume and without Friedmann-like singularities. This manifold was used for calculating coupling constants. Obtaining in this way a theoretical explanation for fundamental forces is at least in the sense of the hierarchy.展开更多
In this paper, we calculate some structure functions of an idealized stellar model, which can be solved by the total mass and radius of a star. These functions have enlightening and pedagogical significance. We find t...In this paper, we calculate some structure functions of an idealized stellar model, which can be solved by the total mass and radius of a star. These functions have enlightening and pedagogical significance. We find that the equation of state of matter is decisive to the fate of a star. Only if the equation of state includes the driving effect of gravity on particles, then it satisfies some increasing and causal conditions and is compatible with Einstein’s field equation. In this case, we always have singularity-free balanced star, no matter how heavy the star is. Usually, we believe that the main factor determining the stellar structure is the pressure equilibrium of the thermonuclear reaction against gravity. But this opinion is inadequate. The calculation of this paper shows that, the pressure generated by the driving effect of gravity on particles is dominant.展开更多
In this paper,the singularity-free predefined-time fuzzy adaptive tracking control problem is studied for non-strict feedback(NSF)nonlinear systems considering mismatched external disturbances.An innovative practical ...In this paper,the singularity-free predefined-time fuzzy adaptive tracking control problem is studied for non-strict feedback(NSF)nonlinear systems considering mismatched external disturbances.An innovative practical predefined-time stability(PPTS)criterion is proposed to provide the theoretical basis for subsequent control design.Compared to the existing predefined-time stability(PTS)criterion,this criterion has a broader application range and can solve the control design issues of nonlinear systems with system uncertainties.Fuzzy logic systems(FLSs)are employed to identify unknown nonlinear functions.Based on the backstepping control technology,a singularity-free predefined-time control(PTC)design method is proposed,in which the hyperbolic tangent function is utilized to avoid the singular problem,and the nature of fuzzy basis function is adopted to resolve the algebraic loop problem.The PPTS of the closed-loop NSF nonlinear system is proven with the Lyapunov theory and the proposed PPTS criterion.Ultimately,the efficiency of the presented PTC design method is verified by several sets of simulations on a single link manipulator system.展开更多
文摘For the stationary Wigner equation with inflow boundary conditions, the numerical convergence with respect to the velocity mesh size are deteriorated due to the singularity at velocity zero. In this paper, using the fact that the solution of the stationary Wigner equation is subject to an integral constraint, we prove that the Wigner equation can be written into a form with a bounded operator B[V]. which is equivalent to the operatorA[V]=θ[V]/v in the original Wigner equation under some conditions. Then the discrete operators discretizing B[V] are proved to be uniformly bounded with respect to the mesh size. Basted on the thcoretical findings, a singularity-free numerical incthod is proposed. Numerical results are provided to show our improved numerical scheme performs much better in numerical convergence than the original scheme based on discretizing A[V].
基金supported in part by the National Natural Science Foundation of China(61903025)the Fundamenta Research Funds for the Central Universities(FRF-GF-18-028B)the China Scholarship Council(201906465028)
文摘This paper investigates the robust relative pose control for spacecraft rendezvous and docking with constrained relative pose and saturated control inputs.A barrier Lyapunov function is used to ensure the constraints of states,so that the computational singularity of the inverse matrix in control command can be avoided,while a linear auxiliary system is introduced to handle with the adverse effect of actuator saturation.The tuning rules for designing parameters in control command and auxiliary system are derived based on the stability analysis of the closed-loop system.It is proved that all closed-loop signals always keep bounded,the prescribed constraints of relative pose tracking errors are never violated,and the pose tracking errors ultimately converge to small neighborhoods of zero.Simulation experiments validate the performance of the proposed robust saturated control strategy.
基金Project supported by the National Key Research and Development Program of China(No.2018YFA0703200)the National Natural Science Foundation of China(Nos.52205594 and51820105008)+1 种基金the China National Postdoctoral Program for Innovative Talents(No.BX20220118)the China Postdoctoral Science Foundation(No.2021M701306)。
文摘The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft robotics,flexible electronics,and biomedicine.Theoretical investigations on large deformations of HMS structures are significant foundations of their applications.This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams.A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact(GE)beam model.The singularity-free governing equations for the three-dimensional(3D)large deformations of an HMS beam are first derived,and then solved with the Galerkin discretization method and the trustregion-dogleg iterative algorithm.The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones.The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples.It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field.The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.
文摘A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work explores the use of the satellite ground-track vector as the differential correction variable.The geodetic latitude is recovered by well-known elementary means.A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed.Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth’s surface,throughout the LEO-GEO range of applications.As a result,a single iteration of the continued fraction iteration yields a maximum error for the satellite height of 10??11 km.and maximum error for the geodetic anomaly of 10??9 rad.The coordinate transformation is completed by non-iteratively recovering the satellite height and the geodetic anomaly.No Taylor expansions are introduced and no Jacobian sensitivity calculations are required.For all practical applications the new algorithm provides a closed-form solution.The accuracy and algorithmic performance of the proposed approach is compared with other state of the art algorithms.
基金Project (Nos. 50375111 and 50675188) supported by the National Natural Science Foundation of China
文摘The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions. Because of the motion un- certainty at singular points, while the manipulator traverses this kind of hypersurface from one singularity-free region to another, its motion cannot be predetermined. In this paper, a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented. First, the singular point transfer disturbance and the pose disturbance, which make the perturbed singular point transfer horizontally and vertically, respectively, are constructed. Through applying these disturbances into the input parameters within the maximum loss control domain, the perturbed persistent configuration is transformed into its corresponding non-persistent one. Under the action of the disturbances, the manipulator can traverse the singularity hypersurface from one singularity-flee region to another with a desired configuration.
文摘In this paper we will see the model of Universe according to Dynamic Universe Model of Cosmology by visualizing various processes that are happening in the Universe as per experimental evidences. For simplifying the matter here, we will see in part 1: about the Galaxy life cycle, where the birth and death of Galaxies discussed. Probably Universe gives guidance for the movement of Galaxies. We call this Part 1: Thinking and Reproducing Universe or Mindless Universe? (Galaxy life cycle). We see every day Sun, Stars, Galaxies etc., dissipating enormous energy in the form of radiation by the way of fusion of Hydrogen to helium. So after sometime all the Hydrogen is spent and Universe will die, is it not? … Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes in frequency and finally will convert into neutrinos (mass). Hence Dynamic Universe Model proposes another process where energy will be converted back into matter and the cycle energy to mass to energy continues, sustaining the Universe to maintain this present status for ever in this form something like a Steady state model without any expansion. This we will see in Part 2: Energy - Mass - Energy Cycle. After converting energy into mass “how various elements are formed and where they are formed?” will be next logical question. Dynamic Universe Model says that these various particles change into higher massive particles or may get bombarded into stars or planets and various elements are formed. Here we bifurcate the formation of elements into 6 processes. They are for Elementary particles and elements generated in frequency changing process, By Cosmic rays, By Small stars, By Large Stars, By Super Novae and Manmade elements By Neutron Stars. This we will discuss in Part 3: Nucleosynthesis.
文摘We propose a model with 3-dimensional spatial sections, constructed from hyperbolic cusp space glued to Seifert manifolds which are in this case homology spheres. The topological part of this research is based on Thurston’s conjecture which states that any 3-dimensional manifold has a canonical decomposition into parts, each of which has a particular geometric structure. In our case, each part is either a Seifert fibered or a cusp hyperbolic space. In our construction we remove tubular neighbourhoods of singular orbits in areas of Seifert fibered manifolds using a splice operation and replace each with a cusp hyperbolic space. We thus achieve elimination of all singularities, which appear in the standard-like cosmological models, replacing them by “a torus to infinity”. From this construction, we propose an alternative manifold for cosmology with finite volume and without Friedmann-like singularities. This manifold was used for calculating coupling constants. Obtaining in this way a theoretical explanation for fundamental forces is at least in the sense of the hierarchy.
文摘In this paper, we calculate some structure functions of an idealized stellar model, which can be solved by the total mass and radius of a star. These functions have enlightening and pedagogical significance. We find that the equation of state of matter is decisive to the fate of a star. Only if the equation of state includes the driving effect of gravity on particles, then it satisfies some increasing and causal conditions and is compatible with Einstein’s field equation. In this case, we always have singularity-free balanced star, no matter how heavy the star is. Usually, we believe that the main factor determining the stellar structure is the pressure equilibrium of the thermonuclear reaction against gravity. But this opinion is inadequate. The calculation of this paper shows that, the pressure generated by the driving effect of gravity on particles is dominant.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.92267203,62373302,62333009,62176111,and 62333004in part by the Key-Area Research and Development Program of Guangdong Province under Grant No.2023B0303030001+2 种基金in part by the Program for Guangdong Introducing Innovative and Entrepreneurial Teams under Grant No.2019ZT08X214in part by the Natural Science Foundation of Shaanxi Province under Grant No.2024JC-YBQN-0663in part by Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University under Grant No.CX2023084。
文摘In this paper,the singularity-free predefined-time fuzzy adaptive tracking control problem is studied for non-strict feedback(NSF)nonlinear systems considering mismatched external disturbances.An innovative practical predefined-time stability(PPTS)criterion is proposed to provide the theoretical basis for subsequent control design.Compared to the existing predefined-time stability(PTS)criterion,this criterion has a broader application range and can solve the control design issues of nonlinear systems with system uncertainties.Fuzzy logic systems(FLSs)are employed to identify unknown nonlinear functions.Based on the backstepping control technology,a singularity-free predefined-time control(PTC)design method is proposed,in which the hyperbolic tangent function is utilized to avoid the singular problem,and the nature of fuzzy basis function is adopted to resolve the algebraic loop problem.The PPTS of the closed-loop NSF nonlinear system is proven with the Lyapunov theory and the proposed PPTS criterion.Ultimately,the efficiency of the presented PTC design method is verified by several sets of simulations on a single link manipulator system.
