This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system...This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.展开更多
This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian sy...This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.展开更多
This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is...This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.展开更多
This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedur...This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps：the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.展开更多
For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for s...For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.展开更多
In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrat...In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.展开更多
The mechanical properties of biological soft tissues are inextricably linked to the field of health care,and their mechanical properties can be important indicators for diagnosing and detecting diseases;they can also ...The mechanical properties of biological soft tissues are inextricably linked to the field of health care,and their mechanical properties can be important indicators for diagnosing and detecting diseases;they can also be used to analyze the causes of organ diseases from a pathological point of view and thus guide the deployment of medical solutions.As an effective method to characterize the mechanical properties of materials,mechanical loading experiments have been successfully applied to the mechanical properties of materials,including tension,compression,pure shear,and so on.Under quasi-static loading,when the material is a biological soft tissue material between a solid and an ideal fluid,its viscoelastic properties strongly respond to the force stimulus,and the stress-strain-time in the elastic phase will have obvious disturbance characteristics.Therefore,the existing statistical methods are often difficult to quantitatively describe the mechanical properties of materials.Therefore,this study proposes an Interval Capture Point based on the principle of integration.The experimental data based on this method can characterize its nonlinear mechanical properties well,especially when the loading speed is extremely low and the soft materials show strong disturbance characteristics.The proposed method can still accurately characterize the hyperelastic and viscoelastic properties of the mechanical properties of biological soft tissues under quasi-static loading.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10272021 and 10572021 and the Doctoral Program Foundation of Institutions of Higher Education of China （Grant No 20040007022）.
文摘This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.
基金Project supported by the National Natural Science Foundation of China(Grant No.10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (10972151)
文摘This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps：the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.
基金The National Natural Science Foundation of China(No.10972151,11272227)
文摘For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.
基金The project supported by the National Natural Science Foundation of China
文摘In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.
基金supported by the National Natural Science Foundation of China[U2241273,12172034,U20A20390,11827803]Beijing Municipal Natural Science Foundation[7212205]the 111 project[B13003]]and the Fundamental Research Funds for the Central Universities.
文摘The mechanical properties of biological soft tissues are inextricably linked to the field of health care,and their mechanical properties can be important indicators for diagnosing and detecting diseases;they can also be used to analyze the causes of organ diseases from a pathological point of view and thus guide the deployment of medical solutions.As an effective method to characterize the mechanical properties of materials,mechanical loading experiments have been successfully applied to the mechanical properties of materials,including tension,compression,pure shear,and so on.Under quasi-static loading,when the material is a biological soft tissue material between a solid and an ideal fluid,its viscoelastic properties strongly respond to the force stimulus,and the stress-strain-time in the elastic phase will have obvious disturbance characteristics.Therefore,the existing statistical methods are often difficult to quantitatively describe the mechanical properties of materials.Therefore,this study proposes an Interval Capture Point based on the principle of integration.The experimental data based on this method can characterize its nonlinear mechanical properties well,especially when the loading speed is extremely low and the soft materials show strong disturbance characteristics.The proposed method can still accurately characterize the hyperelastic and viscoelastic properties of the mechanical properties of biological soft tissues under quasi-static loading.
