In the previous papers I and II, we have studied the difference discrete variational principle and the Euler?Lagrange cohomology in the framework of multi-parameter differential approach. We have gotten the difference...In the previous papers I and II, we have studied the difference discrete variational principle and the Euler?Lagrange cohomology in the framework of multi-parameter differential approach. We have gotten the difference discrete Euler?Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and field theory as well as the difference discrete versions for the Euler?Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the Lagrangian and Hamiltonian formalisms. In this paper, we apply the difference discrete variational principle and Euler?Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms. We will show that either Hamiltonian schemes or Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler?Lagrange cohomological conditions are satisfied.展开更多
In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in vi...In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.展开更多
A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry...A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry structure of Birkhoffian system is discussed, then the symplecticity of Birkhoffian phase flow is presented. Based on these properties we give a way to construct symplectic schemes for Birkhoffian systems by using the generating function method.展开更多
In this second paper of a series of papers, we explore the difference discrete versions for the Euler?Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in...In this second paper of a series of papers, we explore the difference discrete versions for the Euler?Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multi-parameter differential approach. In terms of the difference discrete Euler?Lagrange cohomological concepts, we show that the symplectic or multisymplectic geometry and their difference discrete structure-preserving properties can always be established not only in the solution spaces of the discrete Euler?Lagrange or canonical equations derived by the difference discrete variational principle but also in the function space in each case if and only if the relevant closed Euler?Lagrange cohomological conditions are satisfied.展开更多
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established...We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.展开更多
We derive a formula for double-pulse spectra from closed-orbit theory. We then calculate the double-pulse photodetachment spectra of H<SUP>?</SUP> in the presence of parallel electric and magnetic fields. ...We derive a formula for double-pulse spectra from closed-orbit theory. We then calculate the double-pulse photodetachment spectra of H<SUP>?</SUP> in the presence of parallel electric and magnetic fields. We analyze the spectra in terms of closed-orbits of the system. We suggest a method for the measurement of a phase associated with each closed-orbit.展开更多
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore the...We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire geometric object and the noncommutative differential calculus on regular lattice. In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations, the Euler-Lagrange cohomological concepts and content in the configuration space are employed.展开更多
A general and flexible multi-motif model is proposed based on dynamic programming. By extending theGibbs sampler to the dynamic programming and introducing temperature, an efficient algorithm is developed. Branchpoint...A general and flexible multi-motif model is proposed based on dynamic programming. By extending theGibbs sampler to the dynamic programming and introducing temperature, an efficient algorithm is developed. Branchpoint signalsequences and translation initiation sequences extracted from the rice genome are then examined.展开更多
We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method...We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei <SUP>16</SUP>O and <SUP>208</SUP>Pb, the deformed nucleus <SUP>20</SUP>Ne. Good agreement is obtained.展开更多
We obtained for the Higgs algebra three kinds of single boson realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization, and the unitary Villain-like realization. Th...We obtained for the Higgs algebra three kinds of single boson realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization, and the unitary Villain-like realization. The corre-sponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are given.展开更多
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern Simons form and the Chern density are obtained. Furthermore, the ...In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.展开更多
We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the NN- in S-wave (the qua...We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the NN- in S-wave (the quarks in the nucleons N and N-, and the two nucleons relatively as well, are in S wave) so as to see the possibility if there may be a tight bound state of six quarks as indicated by a strong enhancement at threshold of pp- in J/ψ and B decays. The effective potential which we obtain in terms of the model and approach shows if the experimental enhancement is really caused by a tight S-wave bound state of six quarks, then the quantum number of the bound state is very likely to be I = 1, JPC= 0-+.展开更多
The exotic strange dibaryon particle (ΩΩ)0+ with S = -6 can be produced in relativistic heavy ion collisions. The yields of this kind of exotic strange dibaryon particles can increase signitlcantly soon as the forma...The exotic strange dibaryon particle (ΩΩ)0+ with S = -6 can be produced in relativistic heavy ion collisions. The yields of this kind of exotic strange dibaryon particles can increase signitlcantly soon as the formation of QGP does exhibit after the collision. If there is no phase transition after the collision, the upper bound of the production of this diomega can be estimated from the free hadronic gas model for nuclear matter. The relative yield ratio of diomega to deuteron is less than 0.000205, this means that if there is no QGP creation it is difficult to observe the production of diomega in relativistic heavy ion collisions.展开更多
We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general fe...We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.展开更多
Promising high strangeness dibaryons are studied by the extended quark delocalization and color screeningmodel. It is shown that besides H particle and di-Ω, there might be other dibaryon candidates worth to be searc...Promising high strangeness dibaryons are studied by the extended quark delocalization and color screeningmodel. It is shown that besides H particle and di-Ω, there might be other dibaryon candidates worth to be searchedexperimentally such as NΩ.展开更多
A way to calculate ratios of baryon produced from quark gluon plasma in relativistic heavy ion collisions is presented. It is assumed that at the beginning of the hadronlzation there are diquarks and anti-diquarks in ...A way to calculate ratios of baryon produced from quark gluon plasma in relativistic heavy ion collisions is presented. It is assumed that at the beginning of the hadronlzation there are diquarks and anti-diquarks in the quark matter. The number of three-quark states is distributed between the corresponding multiplets, and hadronic decays are taken into account. The results are shown at last.展开更多
In the light of φ-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed...In the light of φ-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kπ /2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e. the disclination strengths. From the Lagrange's method of multipliers, the equilibrium equation and the molecular field of liquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.展开更多
We in terms of optical theorem estimate the lifetime of B<SUB>c</SUB> meson with the parameters which are determined by fitting the data for the lifetimes and inclusive semileptonic decays of various B and...We in terms of optical theorem estimate the lifetime of B<SUB>c</SUB> meson with the parameters which are determined by fitting the data for the lifetimes and inclusive semileptonic decays of various B and D mesons. In the estimation, we find that the bound-state effects are important, and take them into account carefully in the framework which attributes the effects to the effective masses of the decay heavy quarks in the inclusive processes. We also find that to B<SUB>c</SUB> lifetime the penguin contribution is enhanced due to possible interference between the penguin and the 'tree part' c<SUB>1</SUB>O<SUB>1</SUB> + c<SUB>2</SUB>O<SUB>2</SUB>.展开更多
Magnetic excitations for Ba isotopes are discussed within the nucleon-pair shell model truncated in the SD subspace. With the SD pair determined by a surface- interaction, M1 transitions for are well fitted. The M1 a...Magnetic excitations for Ba isotopes are discussed within the nucleon-pair shell model truncated in the SD subspace. With the SD pair determined by a surface- interaction, M1 transitions for are well fitted. The M1 and M3 transitions for and are also predicted. It is shown that the statement, the collective magnetic properties are due to the orbital motion of nucleons, is approximately valid.展开更多
The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be cal...The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.展开更多
文摘In the previous papers I and II, we have studied the difference discrete variational principle and the Euler?Lagrange cohomology in the framework of multi-parameter differential approach. We have gotten the difference discrete Euler?Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and field theory as well as the difference discrete versions for the Euler?Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the Lagrangian and Hamiltonian formalisms. In this paper, we apply the difference discrete variational principle and Euler?Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms. We will show that either Hamiltonian schemes or Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler?Lagrange cohomological conditions are satisfied.
文摘In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.
基金The project supported by the Special Funds for State Key Basic Research Projects under Grant No.G1999,032800
文摘A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry structure of Birkhoffian system is discussed, then the symplecticity of Birkhoffian phase flow is presented. Based on these properties we give a way to construct symplectic schemes for Birkhoffian systems by using the generating function method.
文摘In this second paper of a series of papers, we explore the difference discrete versions for the Euler?Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multi-parameter differential approach. In terms of the difference discrete Euler?Lagrange cohomological concepts, we show that the symplectic or multisymplectic geometry and their difference discrete structure-preserving properties can always be established not only in the solution spaces of the discrete Euler?Lagrange or canonical equations derived by the difference discrete variational principle but also in the function space in each case if and only if the relevant closed Euler?Lagrange cohomological conditions are satisfied.
基金国家自然科学基金，theState Key Project for Basic Research of China
文摘We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.
文摘We derive a formula for double-pulse spectra from closed-orbit theory. We then calculate the double-pulse photodetachment spectra of H<SUP>?</SUP> in the presence of parallel electric and magnetic fields. We analyze the spectra in terms of closed-orbits of the system. We suggest a method for the measurement of a phase associated with each closed-orbit.
文摘We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire geometric object and the noncommutative differential calculus on regular lattice. In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations, the Euler-Lagrange cohomological concepts and content in the configuration space are employed.
基金the Special Funds for Major National Basic Research Projects，国家自然科学基金
文摘A general and flexible multi-motif model is proposed based on dynamic programming. By extending theGibbs sampler to the dynamic programming and introducing temperature, an efficient algorithm is developed. Branchpoint signalsequences and translation initiation sequences extracted from the rice genome are then examined.
基金The project supported in part by National Natural Science Foundation of China under Grant Nos.10047001,10347113+2 种基金the State Key Basic Research Development Program under Contract No.G200077400the Excellent Young Researcher Grant
文摘We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei <SUP>16</SUP>O and <SUP>208</SUP>Pb, the deformed nucleus <SUP>20</SUP>Ne. Good agreement is obtained.
文摘We obtained for the Higgs algebra three kinds of single boson realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization, and the unitary Villain-like realization. The corre-sponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are given.
文摘In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.
文摘We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the NN- in S-wave (the quarks in the nucleons N and N-, and the two nucleons relatively as well, are in S wave) so as to see the possibility if there may be a tight bound state of six quarks as indicated by a strong enhancement at threshold of pp- in J/ψ and B decays. The effective potential which we obtain in terms of the model and approach shows if the experimental enhancement is really caused by a tight S-wave bound state of six quarks, then the quantum number of the bound state is very likely to be I = 1, JPC= 0-+.
文摘The exotic strange dibaryon particle (ΩΩ)0+ with S = -6 can be produced in relativistic heavy ion collisions. The yields of this kind of exotic strange dibaryon particles can increase signitlcantly soon as the formation of QGP does exhibit after the collision. If there is no phase transition after the collision, the upper bound of the production of this diomega can be estimated from the free hadronic gas model for nuclear matter. The relative yield ratio of diomega to deuteron is less than 0.000205, this means that if there is no QGP creation it is difficult to observe the production of diomega in relativistic heavy ion collisions.
文摘We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.
基金The project supported by National Natural Science Foundation of China under Grant No.90103018
文摘Promising high strangeness dibaryons are studied by the extended quark delocalization and color screeningmodel. It is shown that besides H particle and di-Ω, there might be other dibaryon candidates worth to be searchedexperimentally such as NΩ.
文摘A way to calculate ratios of baryon produced from quark gluon plasma in relativistic heavy ion collisions is presented. It is assumed that at the beginning of the hadronlzation there are diquarks and anti-diquarks in the quark matter. The number of three-quark states is distributed between the corresponding multiplets, and hadronic decays are taken into account. The results are shown at last.
文摘In the light of φ-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kπ /2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e. the disclination strengths. From the Lagrange's method of multipliers, the equilibrium equation and the molecular field of liquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.
文摘We in terms of optical theorem estimate the lifetime of B<SUB>c</SUB> meson with the parameters which are determined by fitting the data for the lifetimes and inclusive semileptonic decays of various B and D mesons. In the estimation, we find that the bound-state effects are important, and take them into account carefully in the framework which attributes the effects to the effective masses of the decay heavy quarks in the inclusive processes. We also find that to B<SUB>c</SUB> lifetime the penguin contribution is enhanced due to possible interference between the penguin and the 'tree part' c<SUB>1</SUB>O<SUB>1</SUB> + c<SUB>2</SUB>O<SUB>2</SUB>.
文摘Magnetic excitations for Ba isotopes are discussed within the nucleon-pair shell model truncated in the SD subspace. With the SD pair determined by a surface- interaction, M1 transitions for are well fitted. The M1 and M3 transitions for and are also predicted. It is shown that the statement, the collective magnetic properties are due to the orbital motion of nucleons, is approximately valid.
基金国家自然科学基金，湖南省自然科学基金，the Scientific Research Foundation of Eduction Burean of Hunan Province
文摘The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.
