The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformati...The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained.An example is given to illustrate the application of the result.展开更多
The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of th...The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of the system are presented. Thirdly, the conditions under which there exists a conserved quantity deduced by the symmetry are obtained. The form of the conserved quantity is the same as that of the constant mass Lagrange system. Finally, an example is shown to illustrate the application of the result.展开更多
By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variab...By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.展开更多
This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are establis...This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results.展开更多
The differential equations of motion of a comtlaint system with parameters and variable mass, of a system with variable mass and servo constraints and those for the control problem on the forced motion of constraint s...The differential equations of motion of a comtlaint system with parameters and variable mass, of a system with variable mass and servo constraints and those for the control problem on the forced motion of constraint systems with variable mass are given respectively. Finally, an example is presented.展开更多
This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total...This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.展开更多
In this paper, a new type of conserved quantity directly deduced from the Mei symmetry for relativistic variable mass system in phase space is studied. The definition and the criterion of the Mei symmetry for the syst...In this paper, a new type of conserved quantity directly deduced from the Mei symmetry for relativistic variable mass system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.展开更多
This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then ...This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.展开更多
Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. ...Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.展开更多
In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. F...In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. Firstly, the dynamics equations are written in the canonical form and the field form. Secondly, the gradient method, the single-component method and the field method are used to integrate the dynamics equations of the corresponding constant mass holonomic system in inertial reference frame respectively. With the restriction of nonholonomic constraints to the initial conditions being considered, the solutions of the dynamics equations of variable mass nonlinear nonholonomic system in noninertial reference frame are obtained.展开更多
In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, an...In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, and Mei conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the results.展开更多
In this paper, Routh 's 'equations for the mechanical systems of the variable mass with nonlinear nonholonomic constraints of arbitrary orders in a noninertial reference system have been deduced not from any v...In this paper, Routh 's 'equations for the mechanical systems of the variable mass with nonlinear nonholonomic constraints of arbitrary orders in a noninertial reference system have been deduced not from any variational principles, but from the dynamical equations of Newtonian mechanics. And then again the other forms of equations for nonholonomic systems of variable mass are obtained from Routh's equations.展开更多
Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new con...Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained, An example is given to illustrate the application of the results.展开更多
Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a ...Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.展开更多
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
Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investi- gated. Appell equations and differential equations of motion for a variable mass holonomic system are estab...Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investi- gated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is given to illustrate the application of the results.展开更多
The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. ...The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.展开更多
The first integrals and their conditions of existence for variable massnonholonomic system in noninertial relerence frames are obtained,and the canonicalequations and the variation equations of the system are extended...The first integrals and their conditions of existence for variable massnonholonomic system in noninertial relerence frames are obtained,and the canonicalequations and the variation equations of the system are extended. It is proved that using the first integral we can construct the integral invariant of the system.Finally,a series of deductions and an example are given.展开更多
Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with varia...Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal oneparameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.展开更多
Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differenti...Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient. condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether. 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
文摘The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained.An example is given to illustrate the application of the result.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10972031)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of the system are presented. Thirdly, the conditions under which there exists a conserved quantity deduced by the symmetry are obtained. The form of the conserved quantity is the same as that of the constant mass Lagrange system. Finally, an example is shown to illustrate the application of the result.
文摘By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
文摘This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results.
文摘The differential equations of motion of a comtlaint system with parameters and variable mass, of a system with variable mass and servo constraints and those for the control problem on the forced motion of constraint systems with variable mass are given respectively. Finally, an example is presented.
基金Project supported by the National Natural Science Foundation of China(Grant No10672143)
文摘This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.
文摘In this paper, a new type of conserved quantity directly deduced from the Mei symmetry for relativistic variable mass system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.
文摘This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.
基金Supported by the Graduate Students' Innovative Foundation of China University of Petrolem (East China) under Grant No.S2009-19
文摘Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.
文摘In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. Firstly, the dynamics equations are written in the canonical form and the field form. Secondly, the gradient method, the single-component method and the field method are used to integrate the dynamics equations of the corresponding constant mass holonomic system in inertial reference frame respectively. With the restriction of nonholonomic constraints to the initial conditions being considered, the solutions of the dynamics equations of variable mass nonlinear nonholonomic system in noninertial reference frame are obtained.
文摘In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, and Mei conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the results.
文摘In this paper, Routh 's 'equations for the mechanical systems of the variable mass with nonlinear nonholonomic constraints of arbitrary orders in a noninertial reference system have been deduced not from any variational principles, but from the dynamical equations of Newtonian mechanics. And then again the other forms of equations for nonholonomic systems of variable mass are obtained from Routh's equations.
文摘Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained, An example is given to illustrate the application of the results.
文摘Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11142014 and 61178032)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10572021)the Preparatory Research Foundation of Jiangnan University,China (Grant No. 2008LYY011)
文摘Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investi- gated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is given to illustrate the application of the results.
基金Supported by the Key Disciplines' Building Foundation of Henan Institute of Educationthe Natural Science Foundation of Education Bureau of Henan Province of China under Grant No. 2009A14003
文摘The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.
文摘The first integrals and their conditions of existence for variable massnonholonomic system in noninertial relerence frames are obtained,and the canonicalequations and the variation equations of the system are extended. It is proved that using the first integral we can construct the integral invariant of the system.Finally,a series of deductions and an example are given.
基金Project supported by the Key Disciplines’ Building Foundation of Henan Institute of Educationthe Natural Science Foundation of Education Bureau of Henan Province,China (Grant No. 2009A140003)the Young Core Instructor from Henan Institute of Education
文摘Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal oneparameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.
文摘Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient. condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether. conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.
