Since there are some problems in the previous cam of deep-fertilization liquid fertilizer applicator,such as poor precision and low-fertilization performance,a method of the contour line of a cam was proposed based on...Since there are some problems in the previous cam of deep-fertilization liquid fertilizer applicator,such as poor precision and low-fertilization performance,a method of the contour line of a cam was proposed based on Matlab GUI development platform.Bernoulli’equation between the liquid fertilizer and the pressure valve of the fertilizer-spraying needle was founded.Moreover,the motion angles of a rise travel and return travel were corrected and the corresponding parameters of the contour line of the cam were obtained.Equations of cam moving from rise travel to return travel were derived according to the simple harmonic motion.In addition,3D model of cam was established by applying the Pro/E software and the rationality of the cam design was verified.The static analysis of the cam was carried out under working conditions and the corresponding dynamics analysis was performed based on D’Alembert’s principle.And then relationships between the binding force and the drag torque were obtained.A bench test indicates that when the pressure of a hydraulic pump is 0.5 MPa and the velocity of a output shaft is 50 r/min,the average consumption of the fertilizer is 19.7 mL for each measurement,which meets the corresponding agronomic requirement,i.e.20 mL.When the rotation angle of the cam is 8.6°and the rise displacement of a plunger is 0.84 mm,the mouth of the fertilizer-spraying needle sprayed liquid fertilizer as soon as it got into the soil and stopped spraying as soon as it got out of the soil.The results show that the designed contour line of the cam meets the requirement,that is,the mouth of the fertilizer-spraying needle should spray liquid fertilizer as soon as it gets into the soil and stop spraying as soon as it gets out of the soil,which meets the agronomic requirements,that is,fertilizer should be sprayed deeply and precisely.And this study lays a theoretical foundation for designing the cam of intermittent type distributor and provides relevant parameters.展开更多
Using d'Alembert equation as the approximation of Einstein's equation, a solution is given in this paper to the time-dependent gravitational equation of the Earth in consideration of the Earth's features, ...Using d'Alembert equation as the approximation of Einstein's equation, a solution is given in this paper to the time-dependent gravitational equation of the Earth in consideration of the Earth's features, which describes the characteristics of pulsation of the Earth and the structures of spherical layers of its interior, thus providing a theoretical basis for establishing the idea of mantle pulsation.展开更多
In high voltage networks for the transport of electrical energy, lightning, a phenomenon as dangerous as it is impressive, with an easily recognizable form, can affect a power line by striking either a phase conductor...In high voltage networks for the transport of electrical energy, lightning, a phenomenon as dangerous as it is impressive, with an easily recognizable form, can affect a power line by striking either a phase conductor, a tower or a guard cable, thus causing more dangerous and constraining stresses on the lines for its proper operation. Thus, this article aims to analyze the behavior of a HV line during an atmospheric discharge and assess the spatial and temporal distribution of the lightning current wave. For this purpose, the generalities on the transmissible power in case of link without resistance and the modeling of the atmospheric surge propagation established on the basis of the theory of the lines with distributed constants implementing the wave equation known as the Alembert equation have been developed. Through this research, we are interested in the study of the space-time distribution of the lightning current wave in order to model the radiated electromagnetic field and to examine the influence of the atmospheric discharge induced overvoltage on the transportable power of a High Voltage AC Transmission line, for a good selective protection in order to illuminate the parasites. The 2D simulation based on engineering and “Transmission Line” models have been developed as well as the verification of the coherence of the different models, by comparing the fractal dimensions of the program results with those of the experimentally obtained figures.展开更多
Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triax...Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.展开更多
According to Newton's dynamical equation of the system of particles, the force is considered to be the function of the coordinate r, velocity and time t, and the various formulae for D'Alembert principle of t...According to Newton's dynamical equation of the system of particles, the force is considered to be the function of the coordinate r, velocity and time t, and the various formulae for D'Alembert principle of the velocity space in both the holonomic and nonholonomic systems are deduced by introducing the concept of kinetic energy in the velocity space (i.e. the accelerated energy).展开更多
A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a ...In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.展开更多
The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group...The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.展开更多
A form invariance of the relativistic Birkhoffian system is studied, and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form i...A form invariance of the relativistic Birkhoffian system is studied, and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form invariance of the system were given. In view of the invariance of relativistic Pfaff_Birkhoff_ D'Alembert principle under the infinitesimal transformation of groups, the theory of Noether symmetries of the relativistic Birkhoffian system were constructed. The relation between the form invariance and the Noether symmetry is studied, and the results show that the form invariance can also lead to the Noether symmetrical conserved quantity of the relativistic Birkhoffian system under certain conditions.展开更多
In this paper, the traditional generalized d'Alembert equations of motion (G_D) in the field of robot dynamics are extended to the circumstances as follows: 1 Considering the robots not only with rotary joi...In this paper, the traditional generalized d'Alembert equations of motion (G_D) in the field of robot dynamics are extended to the circumstances as follows: 1 Considering the robots not only with rotary joints but also with translational joints. 2 Extending the application range of the G_D dynamic equations from the simple chained robots to the tree_structured robots.展开更多
This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is ne...This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.展开更多
基金This research was supported by the National Natural Science Foundation of China(Grant No.51675093)“Young Talents”Project of Northeast Agricultural University(Grant No.18QC19).
文摘Since there are some problems in the previous cam of deep-fertilization liquid fertilizer applicator,such as poor precision and low-fertilization performance,a method of the contour line of a cam was proposed based on Matlab GUI development platform.Bernoulli’equation between the liquid fertilizer and the pressure valve of the fertilizer-spraying needle was founded.Moreover,the motion angles of a rise travel and return travel were corrected and the corresponding parameters of the contour line of the cam were obtained.Equations of cam moving from rise travel to return travel were derived according to the simple harmonic motion.In addition,3D model of cam was established by applying the Pro/E software and the rationality of the cam design was verified.The static analysis of the cam was carried out under working conditions and the corresponding dynamics analysis was performed based on D’Alembert’s principle.And then relationships between the binding force and the drag torque were obtained.A bench test indicates that when the pressure of a hydraulic pump is 0.5 MPa and the velocity of a output shaft is 50 r/min,the average consumption of the fertilizer is 19.7 mL for each measurement,which meets the corresponding agronomic requirement,i.e.20 mL.When the rotation angle of the cam is 8.6°and the rise displacement of a plunger is 0.84 mm,the mouth of the fertilizer-spraying needle sprayed liquid fertilizer as soon as it got into the soil and stopped spraying as soon as it got out of the soil.The results show that the designed contour line of the cam meets the requirement,that is,the mouth of the fertilizer-spraying needle should spray liquid fertilizer as soon as it gets into the soil and stop spraying as soon as it gets out of the soil,which meets the agronomic requirements,that is,fertilizer should be sprayed deeply and precisely.And this study lays a theoretical foundation for designing the cam of intermittent type distributor and provides relevant parameters.
文摘Using d'Alembert equation as the approximation of Einstein's equation, a solution is given in this paper to the time-dependent gravitational equation of the Earth in consideration of the Earth's features, which describes the characteristics of pulsation of the Earth and the structures of spherical layers of its interior, thus providing a theoretical basis for establishing the idea of mantle pulsation.
文摘In high voltage networks for the transport of electrical energy, lightning, a phenomenon as dangerous as it is impressive, with an easily recognizable form, can affect a power line by striking either a phase conductor, a tower or a guard cable, thus causing more dangerous and constraining stresses on the lines for its proper operation. Thus, this article aims to analyze the behavior of a HV line during an atmospheric discharge and assess the spatial and temporal distribution of the lightning current wave. For this purpose, the generalities on the transmissible power in case of link without resistance and the modeling of the atmospheric surge propagation established on the basis of the theory of the lines with distributed constants implementing the wave equation known as the Alembert equation have been developed. Through this research, we are interested in the study of the space-time distribution of the lightning current wave in order to model the radiated electromagnetic field and to examine the influence of the atmospheric discharge induced overvoltage on the transportable power of a High Voltage AC Transmission line, for a good selective protection in order to illuminate the parasites. The 2D simulation based on engineering and “Transmission Line” models have been developed as well as the verification of the coherence of the different models, by comparing the fractal dimensions of the program results with those of the experimentally obtained figures.
文摘Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.
基金the Foundation of Hunan Provincial Educational Com mittee for You
文摘According to Newton's dynamical equation of the system of particles, the force is considered to be the function of the coordinate r, velocity and time t, and the various formulae for D'Alembert principle of the velocity space in both the holonomic and nonholonomic systems are deduced by introducing the concept of kinetic energy in the velocity space (i.e. the accelerated energy).
基金Supported by the Natural Science Foundation of Hubei Province!(992P0 30 7) the National Natural Science Foun-dation of Chi
文摘A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
文摘In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.
文摘The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.
文摘A form invariance of the relativistic Birkhoffian system is studied, and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form invariance of the system were given. In view of the invariance of relativistic Pfaff_Birkhoff_ D'Alembert principle under the infinitesimal transformation of groups, the theory of Noether symmetries of the relativistic Birkhoffian system were constructed. The relation between the form invariance and the Noether symmetry is studied, and the results show that the form invariance can also lead to the Noether symmetrical conserved quantity of the relativistic Birkhoffian system under certain conditions.
文摘In this paper, the traditional generalized d'Alembert equations of motion (G_D) in the field of robot dynamics are extended to the circumstances as follows: 1 Considering the robots not only with rotary joints but also with translational joints. 2 Extending the application range of the G_D dynamic equations from the simple chained robots to the tree_structured robots.
文摘This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.
