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Advancing Hierarchical Equations of Motion for Efficient Evaluation of Coherent Two-dimensional Spectroscopy 被引量:2
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作者 许健 徐瑞雪 +2 位作者 Darius Abramavicius 张厚道 严以京 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2011年第5期497-506,I0003,共11页
To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonli... To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction. 展开更多
关键词 Hierarchical equations of motion Two-dimensional spectroscopy Mixed Heisenberg-Schrodinger scheme
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Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation 被引量:1
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作者 Baofeng JIAO Lingkun RAN +3 位作者 Na LI Ren CAI Tao QU Yushu ZHOU 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2023年第5期856-873,共18页
Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived ... Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system. 展开更多
关键词 generalized Omega equation generalized vertical motion equation Q vector heavy rain
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Forward flight of a model butterfly: Simulation by equations of motion coupled with the Navier-Stokes equations 被引量:7
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作者 Hua Huang Mao Sun 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第6期1590-1601,共12页
The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational f... The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body os- cillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the up- stroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small neg- ative horizontal force, whilst in the upstroke, the body an- gle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizon- tal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-mass- specific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies. 展开更多
关键词 BUTTERFLY Forward flight - Unsteady aerody-namics - equations of motion Navier-Stokes equations
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Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion 被引量:4
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作者 解银丽 贾利群 罗绍凯 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期57-60,共4页
Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations i... Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results. 展开更多
关键词 dynamics of relative motion Appell equations special Lie symmetry Hojman conservedquantity
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Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion 被引量:3
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作者 FEI Chen FEI Wei-yin YAN Li-tan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2019年第2期184-204,共21页
Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been... Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper, by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs. 展开更多
关键词 stochastic differential delay equation (SDDE) SUBLINEAR EXPECTATION EXISTENCE and UNIQUENESS G-Brownian motion stability and BOUNDEDNESS
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Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion 被引量:3
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作者 张美玲 王肖肖 +1 位作者 韩月林 贾利群 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期17-21,共5页
Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass ... Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results. 展开更多
关键词 variable mass relative motion Appell equations Mei conserved quantity
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EQUATIONS OF MOTION FOR NONHOLONOMIC MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS 被引量:1
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作者 张毅 梅凤翔 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第1期59-67,共9页
In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of th... In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given. 展开更多
关键词 analytical mechanics unilateral constraint nonholonomic system equation of motion
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EQUATIONS OF MOTION AND BOUNDARY CONDITIONS OF INCREMENTAL RATE TYPE FOR POLAR CONTINUA 被引量:1
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作者 戴天民 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第3期249-254,共6页
The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equa... The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang. 展开更多
关键词 equations of motion boundary conditions incremental rates polar continua
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CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION 被引量:1
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作者 崔静 闫理坦 《Acta Mathematica Scientia》 SCIE CSCD 2017年第1期108-118,共11页
In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈(1/2,1) in a Hilbert space.We employ the α-norm in order to ... In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈(1/2,1) in a Hilbert space.We employ the α-norm in order to reflect the relationship between H and the fractional power α.Sufficient conditions are established by using stochastic analysis theory and operator theory.An example is provided to illustrate the effectiveness of the proposed result. 展开更多
关键词 stochastic evolution equations fractional Brownian motion CONTROLLABILITY
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AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE
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作者 尹修伟 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期349-362,共14页
In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequal... In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequalities. 展开更多
关键词 integration by parts formula stochastic heat equations fractional Brownian motion shift Harnack inequality coupling by change of measures
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A new method for deriving broad-band polar motion geodetic excitations
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作者 Wei Chen Jiesi Luo +1 位作者 Jim Ray Jiancheng Li 《Geodesy and Geodynamics》 EI CSCD 2024年第5期453-464,共12页
While the geodetic excitationχ(t)of polar motion p(t)is essential to improve our understanding of global mass redistributions and relative motions with respect to the terrestrial frame,the widely adopted method to de... While the geodetic excitationχ(t)of polar motion p(t)is essential to improve our understanding of global mass redistributions and relative motions with respect to the terrestrial frame,the widely adopted method to deriveχ(t)from p(t)has biases in both amplitude and phase responses.This study has developed a new simple but more accurate method based on the combination of the frequency-and time-domain Liouville's equation(FTLE).The FTLE method has been validated not only with 6-h sampled synthetic excitation series but also with daily and 6-h sampled polar motion measurements as well asχ(t)produced by the interactive webpage tool of the International Earth Rotation and Reference Systems Service(IERS).Numerical comparisons demonstrate thatχ(t)derived from the FTLE method has superior performances in both the time and frequency domains with respect to that obtained from the widely adopted method or the IERS webpage tool,provided that the input p(t)series has a length around or more than 25 years,which presents no practical limitations since the necessary polar motion data are readily available.The FTLE code is provided in the form of Mat Lab function. 展开更多
关键词 Earth rotation Polar motion Geodetic excitation Liouville's equation Mat Lab
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Dynamic flight stability of hovering model insects:theory versus simulation using equations of motion coupled with Navier-Stokes equations 被引量:9
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作者 Yan-Lai Zhang Mao Sun 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2010年第4期509-520,共12页
In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model ... In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model (which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings' degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments); the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency (164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency (26 Hz). The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low (the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large) compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects. 展开更多
关键词 Insect Hovering Dynamic flight stability Averaged model equations-of-motion Navier-Stokes simulation
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Impact of singularity of Navier-Stokes equation upon atmospheric motion equations
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作者 施惟慧 王曰朋 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第5期689-693,共5页
Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic... Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations. 展开更多
关键词 equations of atmospheric approximation stability singular equation motion Navier-Stokes equation BOUSSINESQ
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Monolithic Coupling of the Pressure and Rigid Body Motion Equations in Computational Marine Hydrodynamics
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作者 Hrvoje Jasak Inno Gatin Vuko Vukcevic 《Journal of Marine Science and Application》 CSCD 2017年第4期375-381,共7页
In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned man... In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy. 展开更多
关键词 MONOLITHIC COUPLING pressure equation rigid body motion COMPUTATIONAL fluid dynamics MARINE HYDRODYNAMICS SEAKEEPING
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A FIELD METHOD FOR INTEGRATING THE EQUATIONS OF MOTION OF NONHOLONOMIC CONTROLLABLE SYSTEMS
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作者 梅凤翔 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第2期181-187,共7页
This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.
关键词 equation of motion nonhonolomic system controllable system field method
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ONE TYPE OF INTEGRALS FOR THE EQUATIONS OF MOTION OF HIGHER-ORDER NONHOLONOMIC SYSTEMS
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作者 梅凤翔 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第8期799-806,共8页
This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and... This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method. 展开更多
关键词 equations of motion INTEGRAL higher-order nonholonomic system
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On a Compound Poisson Risk Model Perturbed by Brownian Motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time
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作者 Delwendé Abdoul-Kabir Kafando Kiswendsida Mahamoudou Ouedraogo Pierre Clovis Nitiema 《Open Journal of Statistics》 2024年第1期1-37,共37页
This paper considers the compound Poisson risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance... This paper considers the compound Poisson risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance company’s portfolio is governed by two classes of policyholders. On the one hand, the first class where the amount of claims is high, and on the other hand, the second class where the amount of claims is low, this difference in claim amounts has significant implications for the insurance company’s pricing and risk management strategies. When policyholders are in the first class, they pay an insurance premium of a constant amount c<sub>1</sub> and when they are in the second class, the premium paid is a constant amount c<sub>2</sub> such that c<sub>1 </sub>> c<sub>2</sub>. The nature of claims (low or high) is measured via random thresholds . The study in this work will focus on the determination of the integro-differential equations satisfied by Gerber-Shiu functions and their Laplace transforms in the risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. . 展开更多
关键词 Gerber-Shiu Function Copula Integro-Differential equation Laplace Trans-form Brownian motion
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KANE’S EQUATIONS FOR PERCUSSION MOTION OF VARIABLE MASS NONHOLONOMIC MECHANICAL SYSTEMS
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作者 张耀良 乔永芬 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第9期839-850,共12页
In this paper,the Kane’s equations for the Routh’s form of variable massnonholonomic systems are established.and the Kane’s equations for percussion motionof variable mass holonomic and nonholonomic systems are d... In this paper,the Kane’s equations for the Routh’s form of variable massnonholonomic systems are established.and the Kane’s equations for percussion motionof variable mass holonomic and nonholonomic systems are deduced from them. Secondly,the equivalence to Lagrange’s equations for percussion motion and Kane’sequations is obtained,and the application of the new equation is illustrated by anexample. 展开更多
关键词 variable mass percussion motion Kane’s equation nonholonomic system
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Analytical solution of basic equations set of atmospheric motion
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作者 施惟慧 沈春 王曰朋 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第3期385-394,共10页
On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the thi... On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper. 展开更多
关键词 basic equations set of atmospheric motion structure of solution space analytical solution
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Higher-order differential variational principle and differential equations of motion for mechanical systems in event space
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作者 张相武 李院院 +1 位作者 赵小侠 罗文峰 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第10期292-298,共7页
In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the... In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained. 展开更多
关键词 event space the higher-order d'Alembert-Lagrange principle the higher-order time rate of changeof force the higher-order differential equations of motion
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