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1.
Lie symmetries and conserved quantities of nonconservative nonholonomic systems in phase space 总被引:1,自引:0,他引:1
The invariance and conserved quantities of the nonconservative nonholonomic systems are studied by introducing the infinitesimal transformations in phase space.The Lie’s symmetrical determining equations are establish ed.The Lie’s symmetrical structure equation is obtained.An example to illustrate the application of the result is given. 相似文献
2.
相空间中有二阶线性单面约束的非完整系统的Lie对称性与守恒量 总被引:4,自引:0,他引:4
研究相空间中有二阶线性单面约束的非完整系统的Lie对称性与守恒量。首先根据微分方程在无限小变换下的不变性建立Lie对称性所满足的确定方程和限制方程,给出结构方程和守恒量;其次讨论系统的Lie对称性逆问题。最后举一实例说明结果的应用。 相似文献
3.
The conditions for determining solution of buckling eigenvalue problem are discussed. The corresponding system of integral
equations with constraint conditions and boundary variational equations with Lagrange multiplier are established. The theorems
on the existence and uniqueness of the solution for these problems are given. The corresponding boundary element method is
constructed and the error estimation for the approximation solution is obtained. Finally the numerical example is given.
Foundation item: the National Natural Science Foundation Pre-research Project (T4107015)
Biography: Ding Rui (1969-) 相似文献
4.
IntroductionThestudyofsymmetryandconservedquantityofmechanicalsystemisanimportanttopicinmathematics,mechanicsandphysics .ThemoderntheoriesofsymmetryandconservedquantityofmechanicalsystemincludeNoethersymmetrytheoryandLiesymmetrytheory .In 1979M .Lutzkyando… 相似文献
5.
IntroductionIn1979,R.BengtssonandS.Franendorfaccuratlymeasuredthemaximumvaluesofthespinvelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvalueofthespinvelocityofonenucleonwasdifferenttothoseoftheothers[1].Withthedevelopmentofscienceandtechnology,… 相似文献
6.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(11):1253-1258
The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua
based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations
of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete
principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived
from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different
from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics
may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results
of micropolar thermopiezoelectricity are directly given.
Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931-) 相似文献
7.
CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)-LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS 总被引:2,自引:0,他引:2
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot’s equations for saturated porous media. The Darcy’s laws of unsaturated soil were proved. It is shown that Biot’s equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational. 相似文献
8.
IntroductionForseveralhundredyears,ithasbeenbothimportantanddifficultprojecttoconstructtheanalyticalsolutionsfornonlineardifferentialequations.Manymathematiciansandtheoreticalphysicistshavedonealotofwork[1~ 5 ].However,thereexistlotsofimportantandbeingofp… 相似文献
9.
The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed.
And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed
initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist
any unique solution.
Foundation item: the National Natural Science Foundation of China (19971054)
Biography: Shen Zhen (1977−) 相似文献
10.
RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅱ)-THERMOPIEZOELECTRICITY AND MAGNETOTHERMOELASTICITY 总被引:1,自引:1,他引:1
The theories of thermopiezoelectricity and magnetoelasticity for micropolar continua have been systematically developed by
W. Nowacki. In this paper, the theories are restudied. The reason why they were restricted to linear cases is analyzed. The
more general conservation principle of energy, energy balance equation and Hamilton principle of thermopiezoelectricity and
magnetoelasticity for micropolar continua are established. The corresponding complete equations of motion and boundary conditions
as well as balance equations of energy rate for local and nonlocal micropolar thermopiezoelectricity and magnetothermoelasticity
are naturally derived. By means of two new functionals and total variation the boundary conditions of displacement, microrotation,
electric potential and temperature are also given.
Foundation item: the National Natural Science Foundation of China (10072024); the International Cooperation Project of the NSFC (10011130235)
and the DFG (51520001); the Research Foundation of the Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931-) 相似文献
11.
Shen Zhen 《应用数学和力学(英文版)》2003,24(5):545-554
The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification
theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods
of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial
value problem on hyper plane {t=0} in R4, and explain that the problem has more than one solution.
Foundation item: the National Natural Science Foundation of China (19971054)
Biography: Shen Zhen (1977−) 相似文献
12.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(10):1134-1140
The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether’s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics. The new concrete forms of various conservation laws of couple stress elasticity are derived. The precise nature of these conservation laws which result from the given invariance requirements are established. Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper. 相似文献
13.
Noether conserved quantities and Mei symmetries for non-conservative Hamiltonian difference systems with irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie point transformations acting on the lattice, as well as the difference equations, and the determining equations of Mei symmetries are obtained for the systems. The discrete versions of Noether conserved quantity are constructed by the Mei symmetries. An example is presented to illustrate the results. 相似文献
14.
For a weakly nonholonomic system, the Lie symmetry and approximate Hojman conserved quantity of Appell equations are studied. Based on the Appell equations for a weakly nonholonomic system under special infinitesimal transformations of a group in which the time is invariable, the definition of the Lie symmetry of the weakly nonholonomic system and its first-degree approximate holonomic system are given. With the aid of the structure equation that the gauge function satisfies, the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are derived. Finally, an example is given to study the exact and approximate Hojman conserved quantity of the system. 相似文献
15.
The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear
evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence
and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to
the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear
evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence
and uniqueness of local solution presented by YUAN Zhong-xin.
Contributed by Chen Yu-shu
Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation
of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University
Biography: Chen Fang-qi (1963-) 相似文献
16.
In this paper, we present a new kind of fractional dynamical equations, i.e., the fractional generalized Hamiltonian equations in terms of combined Riesz derivatives, and it is proved that the fractional generalized Hamiltonian system possesses consistent algebraic structure and Lie algebraic structure, and the Poisson conservation law of the fractional generalized Hamiltonian system is investigated. Then the conditions, which a fractional generalized Hamiltonian system can be reduced to a generalized Hamiltonian system, a fractional Hamiltonian system and a Hamiltonian system are given. Further, the conserved quantities of a fractional dynamical system are given to illustrate the method and results of the application. At last, a new fractional Volterra model of the three species groups is presented and its conserved quantities are obtained, by using the method of this paper. 相似文献
17.
Lie symmetries and conserved quantities of second-order nonholonomic mechanical system 总被引:3,自引:0,他引:3
方建会 《应用数学和力学(英文版)》2002,23(9):1105-1110
The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal transformations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly , the inverse problems of the Lie symmetries are studied . Finally , an example is given to illustrate the application of the result. 相似文献
18.
CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)-NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS 总被引:1,自引:1,他引:1
The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory.
The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic
assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived.
Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive
equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum,
the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given,
and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.
Foundation items: the National Natural Science Foundation of China (59678003); Special Research Plan of the Education Department of Shaanxi
Province (01JK178)
Biographies: HUANG Yi (1936-) ZHANG Yin-ke (1964-) 相似文献
19.
Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the definition of fractional generalized quasi-symmetry is given, the criteria of fractional generalized quasi-symmetry and the corresponding conserved quantity are achieved for fractional generalized Birkhoffian systems. Thirdly, perturbation to symmetry and adiabatic invariants for disturbed fractional generalized Birkhoffian systems are presented. Finally, an example is given to illustrate the results. 相似文献
20.
Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisymmetric
vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry
elastic layer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a
pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration
of mixed boundary-value condition. The results are reduced to the case for saturated half-space. The set of dual integral
equations are reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Numerical examples
are given at the end of the paper and plots of the dynamic compliance coefficient Cv versus the dimensionless frequency a0 are presented.
Foundation item: the National Natural Science Foundation of China (59579018)
Biography: CHEN Sheng-li (1974-) 相似文献