In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia. This equation is the generalization of e...In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia. This equation is the generalization of equations of motion for the corresponding thick elastic plate, and it can be degenerated into several types of equations for various special cases.展开更多
A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C. A. Murray[1]
In the standard Einstein-Cartan theory,matter fields couple to gravity through the Minimal Coupling Procedure(MCP),and yet leave the theory an ambiguity.Applying MCP to the action or to the equation of motion would le...In the standard Einstein-Cartan theory,matter fields couple to gravity through the Minimal Coupling Procedure(MCP),and yet leave the theory an ambiguity.Applying MCP to the action or to the equation of motion would lead to different gravitational couplings.We propose a new covariant derivative to remove the ambiguity and discuss the relation between our proposal and previous treatments on this subject.展开更多
In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of th...In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.展开更多
We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the firs...We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.展开更多
This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.
The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational f...The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body os- cillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the up- stroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small neg- ative horizontal force, whilst in the upstroke, the body an- gle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizon- tal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-mass- specific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.展开更多
The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equa...The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.展开更多
This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and...This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method.展开更多
In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the...In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.展开更多
This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in ves...This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in vestigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D Alambert-Le range, Hamilton-Ostrogradski and Gauss.展开更多
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
The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the speci...The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.展开更多
In this paper,with Poincare's formalism,and an indirect method,the canonical forms of the generalized equations of motion due to Nielsen and Cenov of a holonomic dynamical system in the velocity-phase space and th...In this paper,with Poincare's formalism,and an indirect method,the canonical forms of the generalized equations of motion due to Nielsen and Cenov of a holonomic dynamical system in the velocity-phase space and the acenleration-phase space are obtained in terms of the Poincare parameters.展开更多
This paper first reduces the motion equation of a collapsible tube to the Mathieu equation with damping. Then the stability charts correcting the accuracy to each order are obtained with the method of asymptotic expan...This paper first reduces the motion equation of a collapsible tube to the Mathieu equation with damping. Then the stability charts correcting the accuracy to each order are obtained with the method of asymptotic expansions. The accuracy of the results obtained with the average variational method is shown. And some phenomena observed in the experiment are also explained.展开更多
Based on the dynamic theory of multi-rigid body system, the mathematical model of dynamics and impact dynamics of the bullet belt of airplane gun was established. Then, the numerical and graphic simulation of the moti...Based on the dynamic theory of multi-rigid body system, the mathematical model of dynamics and impact dynamics of the bullet belt of airplane gun was established. Then, the numerical and graphic simulation of the motion of the bullet belt were carried out.展开更多
Different multidisciplinary design optimization (MDO) problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the...Different multidisciplinary design optimization (MDO) problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the referred vehicle, three disciplines have been considered, which are trajectory, propulsion and aerodynamics. A special design structure matrix is developed to assist data exchange between disciplines. This design process uses response surface method (RSM) for multidisciplinary optimization of the rocket. The RSM is applied to the design in two categories: the propulsion model and the system level. In the propulsion model, RSM determines an approximate mathematical model of the engine output parameters as a function of design variables. In the system level, RSM fits a surface of objective function versus design variables. In the first MDO problem formulation, two design variables are selected to form propulsion discipline. In the second one, three new design variables from geometry are added and finally, an optimization method is applied to the response surface in the system level in order to find the best result. Application of the first developed multidisciplinary design optimization procedure increased accessible altitude (performance index) of the referred sounding rocket by twenty five percents and the second one twenty nine.展开更多
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established. The material of the beams obeys the Leaderman nonlinear constitutive relation. rn the ca...The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established. The material of the beams obeys the Leaderman nonlinear constitutive relation. rn the case of two simply supported ends, the mathematical model is simplified into an integro-differential equation after a 2nd-order truncation by the Galerkin method. Then the equation is further reduced to an ordinary differential equation which is convenient to carry out numerical experiments. Finally, the dynamical behavior of Ist-order and 2nd-order truncation are numerically compared.展开更多
The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics' of the rotational systems is constructed. The relativistic generalized kinetic energy function for ...The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics' of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems [GRAPHICS] and the generalized acceleration energy function [GRAPHICS] are constructed, and furthermore, the Hamilton principle and three kinds of D'Alembert principles are given. For the systems with holonomic constraints, the relativistic Lagrange equation, Nielsen equation, Appell equation and Hamilton canonical equation of the rotational systems are constructed; For the systems with nonholonomic constraints, the relativistic Routh equation, Chaplygin equation, Nielsen equation and Appell equation of the rotational systems are constructed; the relativistic Noether conservation law of the rotational systems are given too.展开更多
The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for ra...The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case.展开更多
文摘In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia. This equation is the generalization of equations of motion for the corresponding thick elastic plate, and it can be degenerated into several types of equations for various special cases.
文摘A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C. A. Murray[1]
基金supported by the China NSF via Grants No.11535005 and No.11275077。
文摘In the standard Einstein-Cartan theory,matter fields couple to gravity through the Minimal Coupling Procedure(MCP),and yet leave the theory an ambiguity.Applying MCP to the action or to the equation of motion would lead to different gravitational couplings.We propose a new covariant derivative to remove the ambiguity and discuss the relation between our proposal and previous treatments on this subject.
文摘In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.
文摘We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.
文摘This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.
基金supported by the National Natural Science Foundation of China(11232002)the Ph.D.Student Foundation of Chinese Ministry of Education(30400002011105001)
文摘The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body os- cillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the up- stroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small neg- ative horizontal force, whilst in the upstroke, the body an- gle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizon- tal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-mass- specific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.
文摘The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.
文摘This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method.
基金Project supported by the Science and Technology Program of Xi’an City,China(Grant No.CXY1352WL34)
文摘In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.
文摘This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in vestigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D Alambert-Le range, Hamilton-Ostrogradski and Gauss.
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.
文摘The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.
基金This paper was presented at the International Congress of Mathematicians(ICM),21—29 August,1990,Kyoto University,Japan.
文摘In this paper,with Poincare's formalism,and an indirect method,the canonical forms of the generalized equations of motion due to Nielsen and Cenov of a holonomic dynamical system in the velocity-phase space and the acenleration-phase space are obtained in terms of the Poincare parameters.
文摘This paper first reduces the motion equation of a collapsible tube to the Mathieu equation with damping. Then the stability charts correcting the accuracy to each order are obtained with the method of asymptotic expansions. The accuracy of the results obtained with the average variational method is shown. And some phenomena observed in the experiment are also explained.
文摘Based on the dynamic theory of multi-rigid body system, the mathematical model of dynamics and impact dynamics of the bullet belt of airplane gun was established. Then, the numerical and graphic simulation of the motion of the bullet belt were carried out.
文摘Different multidisciplinary design optimization (MDO) problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the referred vehicle, three disciplines have been considered, which are trajectory, propulsion and aerodynamics. A special design structure matrix is developed to assist data exchange between disciplines. This design process uses response surface method (RSM) for multidisciplinary optimization of the rocket. The RSM is applied to the design in two categories: the propulsion model and the system level. In the propulsion model, RSM determines an approximate mathematical model of the engine output parameters as a function of design variables. In the system level, RSM fits a surface of objective function versus design variables. In the first MDO problem formulation, two design variables are selected to form propulsion discipline. In the second one, three new design variables from geometry are added and finally, an optimization method is applied to the response surface in the system level in order to find the best result. Application of the first developed multidisciplinary design optimization procedure increased accessible altitude (performance index) of the referred sounding rocket by twenty five percents and the second one twenty nine.
文摘The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established. The material of the beams obeys the Leaderman nonlinear constitutive relation. rn the case of two simply supported ends, the mathematical model is simplified into an integro-differential equation after a 2nd-order truncation by the Galerkin method. Then the equation is further reduced to an ordinary differential equation which is convenient to carry out numerical experiments. Finally, the dynamical behavior of Ist-order and 2nd-order truncation are numerically compared.
文摘The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics' of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems [GRAPHICS] and the generalized acceleration energy function [GRAPHICS] are constructed, and furthermore, the Hamilton principle and three kinds of D'Alembert principles are given. For the systems with holonomic constraints, the relativistic Lagrange equation, Nielsen equation, Appell equation and Hamilton canonical equation of the rotational systems are constructed; For the systems with nonholonomic constraints, the relativistic Routh equation, Chaplygin equation, Nielsen equation and Appell equation of the rotational systems are constructed; the relativistic Noether conservation law of the rotational systems are given too.
文摘The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case.