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Lie Symmetries and Conserved Quantities of Holonomic Mechanical Systems in Terms of Quasi-Coordinatee 被引量:1
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作者 傅景礼 刘荣万 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 1998年第3期215-220,共6页
Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in te... Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in terms of quasi-coordinates was given. Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equations of the Lie symmetries of holonomic mechanical systems in terms of quassi-coordinates are established. The structure equation and the form of conserved quantities are obtained. An example to illustrate the applicaiton of the result is given. 展开更多
关键词 analytical mechanics quasi-coordinate Lie symmetry conserved quantity
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Lie Symmetries and Conserved Quantities of Systems of Relative Motion Dynamics
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作者 刘荣万 傅景礼 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 1998年第3期221-225,共5页
Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations u... Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given. 展开更多
关键词 analytical mechanics dynamical of relative motion Lie symmetry conserved quantity
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On the Lie Symmetries of the NonholonomicMechanical Systems 被引量:2
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作者 吴润衡 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 1997年第3期229-235,共7页
The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the applic... The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the application of the results are provided. 展开更多
关键词 analytical mechanics nonholonomic system Lie symmetry conservation las
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Conserved quantities from Lie symmetries for nonholonomic systems 被引量:2
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作者 张毅 薛纭 《Journal of Southeast University(English Edition)》 EI CAS 2003年第3期289-292,共4页
This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are es... This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result. 展开更多
关键词 analytical mechanics nonholonomic system SYMMETRY conserved quantity
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Lie Symmetries and Conserved Quantities of Holonomic Systems with Remainder Coordinates 被引量:1
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作者 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 1998年第1期26-31,共6页
Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformati... Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result. 展开更多
关键词 analytical mechanics remainder coordinate Lie symmetry conserved quantity
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Form Invariance of Lagrange System 被引量:57
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作者 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 2000年第2期120-124,共5页
To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relati... To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established. 展开更多
关键词 analytical mechanics Lagrange system form invariance Noether symmetry
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Biomimetic asymmetric Michael addition reactions in water catalyzed by amino-containing β-cyclodextrin derivatives 被引量:4
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作者 朱庆英 沈海民 +1 位作者 杨祖金 纪红兵 《Chinese Journal of Catalysis》 SCIE EI CAS CSCD 北大核心 2016年第8期1227-1234,共8页
Nineβ‐cyclodextrin derivatives containing an amino group were synthesized via nucleophilic sub‐stitution from mono(6‐O‐p‐tolylsulfonyl)‐β‐cyclodextrin and used in asymmetric biomimetic Mi‐chael addition re... Nineβ‐cyclodextrin derivatives containing an amino group were synthesized via nucleophilic sub‐stitution from mono(6‐O‐p‐tolylsulfonyl)‐β‐cyclodextrin and used in asymmetric biomimetic Mi‐chael addition reactions in water at room temperature. The mechanism responsible for the moder‐ate activity and enantioselectivity of the β‐cyclodextrin derivatives was explored using nuclear magnetic resonance spectroscopy, namely 2D 1H rotating‐frame overhauser effect spectroscopy (ROESY), ultraviolet absorption spectroscopy, and quantum chemical calculations, which provide a useful technique for investigating the formation of inclusion complexes. The effects of the pH of the reaction medium, theβ‐cyclodextrin derivative dosage, the structure of the modifying amino group, and various substrates on the yield and enantioselectivity were investigated. The results indicated that these factors had an important effect on the enantiomeric excess (ee) in the reaction system. Experiments using a competitor for inclusion complex formation showed that a hydrophobic cavity is necessary for enantioselective Michael addition. A comparison of the reactions using 4‐nitro‐β‐nitrostyrene and 2‐nitro‐β‐nitrostyrene showed that steric hindrance improved the enan‐tioselectivity. This was verified by the optimized geometries obtained from quantum chemical cal‐culations. An ee of 71%was obtained in the asymmetric Michael addition of cyclohexanone and 2‐nitro‐β‐nitrostyrene, using (S)‐2‐aminomethylpyrrolidine‐modified β‐CD as the catalyst, in an aqueous buffer solution, i.e., CH3COONa‐HCl (pH 7.5). 展开更多
关键词 Β-CYCLODEXTRIN MODIFICATION Enantioselective Michael addition Quantum chemistry calculation
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Form Invariance of Routh Equations
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作者 王树勇 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 2002年第3期329-331,共3页
The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with ... The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed. 展开更多
关键词 analytical mechanics form invariance Noether symmetry Lie symmetry
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Hidden Symmetries for Thermodynamics and Emergence of Relativity 被引量:1
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作者 赵柳 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第10期641-646,共6页
Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherprob... Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity. 展开更多
关键词 emergent gravity THERMODYNAMICS GEOMETRY principle of relativity
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A mathematical model of symmetry based on mathematical definition 被引量:3
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作者 刘玉生 杨将新 +1 位作者 吴昭同 高曙明 《Journal of Zhejiang University Science》 CSCD 2002年第1期24-29,共6页
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types,... Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis. 展开更多
关键词 mathematical definition symmetry tolerance mathematical model CAD/CAM production engineering
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Properties of a Bound Polaron under a Perpendicular Magnetic Field 被引量:3
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作者 LIU Jia XIAO Jing-Lin +1 位作者 HUO Shu-Fen CHEN Zi-Yui 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第5X期930-934,共5页
We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state bin... We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit (SO) interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron's, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected. 展开更多
关键词 asymmetric heterostructures SPINTRONICS Rashba spin-orbit interaction
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Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems 被引量:2
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作者 DING Ning FANG Jian-Hui WANG Peng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第4期594-596,共3页
Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system witho... Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system without perturbation are given. The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained. 展开更多
关键词 Mei symmetry PERTURBATION adiabatic invariant nonholonomic mechanical system
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An Optical Disdrometer for Measuring Present Weather Parameters
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作者 JIA Sheng-Jie Lü Da-Ren XUAN Yue-Jian 《Atmospheric and Oceanic Science Letters》 CSCD 2014年第6期559-563,共5页
A new present weather identifier(PWI) based on occlusion and scattering techniques is presented in the study. The present weather parameters are detectable by the meteorological optical range(MOR) approximately up to ... A new present weather identifier(PWI) based on occlusion and scattering techniques is presented in the study. The present weather parameters are detectable by the meteorological optical range(MOR) approximately up to 50 km and by droplets with diameters ranging from 0.125 mm to 22 mm with velocities up to 16 m s-1. The MOR error is less than 8% for the MOR within 10 km and less than 15% for farther distances. Moreover, the size errors derived from various positions of the light sheet by the particles were checked within ± 0.1 mm ± 5%. The comparison shows that the MOR, in a sudden shower event, is surprisingly consistent with those of the sentry visibility sensors(SVS) with a correlation coefficient up to 98%. For the rain amounts derived from the size and velocity of the droplets, the daily sums by the PWI agree within 10% of those by the Total Rain Weighing Sensor(TRwS205) and the rain gauge. Combined with other sensors such as temperature, humidity, and wind, the PWI can serve as a present weather sensor to distinguish several weather types such as fog, haze, mist, rain, hail, and drizzle. 展开更多
关键词 present weather parameters present weather identifier precipitation measurement hydrometeor classification meteorological optical range
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Critical Mass of Gauge Boson in Rainbow QED3 被引量:1
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作者 FENGHong-Tao HUFei +1 位作者 SUNWei-Min ZONGHong-Shi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第3期501-503,共3页
In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the ... In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparision with the previous results is presented. 展开更多
关键词 QED_3 dynamical chiral symmetry breaking critical gauge boson mass
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Dynamic performance of six-axle locomotive subjected to asymmetric brake shoe forces 被引量:2
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作者 LIU Peng-fei ZHANG Kai-long CAO Yun-qiang 《Journal of Central South University》 SCIE EI CAS CSCD 2020年第9期2776-2791,共16页
To research the influence of asymmetric brake shoe forces(ABSF)induced by braking failure on the dynamic performance of six-axle locomotive,the static equilibrium model of three-axle bogie and dynamic model for locomo... To research the influence of asymmetric brake shoe forces(ABSF)induced by braking failure on the dynamic performance of six-axle locomotive,the static equilibrium model of three-axle bogie and dynamic model for locomotive are established.The coupling vibration equations of axle hung motor and wheelset are derived.For the air braking,the influence mechanism of ABSF on the wheel-rail asymmetric motion and force characteristics are discussed.It can be found that if the ABSF is applied in the front wheelset,all the wheelsets move laterally in the same direction.Once the ABSF occurs in the middle or rear one,other wheelsets may move laterally towards the opposite direction.The motion amplitude and direction of all wheelsets strictly depend on the resultant moment of suspension yawing moment and brake shoe asymmetric moment.For the asymmetric braking,the free lateral gap of axle-box could increase the wheelset motion amplitude,but could not change the moving direction.In both the straight line and curve,the ABSF may lead to wheelset misaligning motion,intensify the wheel-rail lateral dynamic interaction and deteriorate wheel-rail contact state.Especially for the steering wheelsets,the asymmetric braking increases the wheelset attack angle significantly,which forms the worst braking condition. 展开更多
关键词 LOCOMOTIVE brake shoe force dynamic performance asymmetric braking wheel-rail contact
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Lie Symmetry and Conserved Quantities for Nonholonomic Vacco Dynamical Systems 被引量:2
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作者 DING Ning FANG Jian-Hui 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第2X期265-268,共4页
In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity... In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained. 展开更多
关键词 Vacco dynamical system Lie symmetry general Hojman conserved quantity Lutzky conserved quantity
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Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations 被引量:1
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作者 QU Chang-Zheng KANG Jing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第1期9-16,共8页
In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie po... In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded. 展开更多
关键词 symmetry group system of nonlinear diffusion equation nonlocal symmetry
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ANALYTIC STUDY ON POTENTIAL INSTABILITY AND SPIRAL STRUCTURE OF RAIN CLUSTERS 被引量:3
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作者 于杰 张铭 《Journal of Tropical Meteorology》 SCIE 2011年第1期79-86,共8页
This paper presents a study on potential instability and spiral structure of unstable rain clusters.First,we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinat... This paper presents a study on potential instability and spiral structure of unstable rain clusters.First,we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinates and acquire its analytic solution.Second,we discuss the potential instability of non-axisymmetrical rain clusters.Finally,we conclude that spiral structures can exist in rain clusters.Our analysis indicates that potential instability occurs when humid stratification coefficient is less than zero.Unstable growth rate increases with the increase of the absolute value for humid stratification coefficient.The simpler the vertical structure of perturbation,the thicker the inversion layer;additionally,the smaller the radius of the rain clusters,the larger the unstable growth rate.Simulation results agree well with those from observation and forecast.The spiral structure simulated by our model is similar to a radar echo,suggesting that rain clusters with spiral structures can occur in the atmosphere.In addition,they are generally close to the model solution in this work. 展开更多
关键词 rain clusters mathematic model spiral structure potential instability
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Biased Motion in a Symmetric Periodic Potential by Breaking Temporal Sysmmetry
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作者 ZHENGZhi-Gang LIXiao-Wen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2001年第2期151-156,共6页
Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied. With a collaboration of the potential field and the asymmetric ac... Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied. With a collaboration of the potential field and the asymmetric ac force, a dc current can be observed. Resonant current steps are found for a finite period of the ac force. A phase diagram of these resonant steps is given. Stochastic-resonance-like directional transport induced by thermal noises is revealed. 展开更多
关键词 RATCHET directional transport stochastic resonance
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Functional Separable Solutions of Nonlinear Heat Equations in Non-Newtonian Fluids 被引量:1
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作者 GOU Ming QU Chang-Zheng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期257-262,共6页
We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables... We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained. 展开更多
关键词 group foliation method functional separation of variable nonlinear heat equation symmetry group
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