Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was...Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was determined. Results and Conclusion The equations a Lie algebraic structure if any nonpotential generalized force doesn't exist while while the equations possess a Lie-admissible algebraic structure if nonpotential generalized forces exist .展开更多
In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same...In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.展开更多
This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exist...This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.展开更多
This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding confor...This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.展开更多
Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized g...Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of the holonomic system. Some examples are given to illustrate the application of the results.展开更多
For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,...For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.展开更多
In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic syst...In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.展开更多
Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomi...Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.展开更多
For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of tile theory of i...For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of tile theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and qs. An example is given to illustrate the application of the results.展开更多
In this paper,a comparative study of the path planning problem using evolutionary algorithms,in comparison with classical methods such as the A*algorithm,is presented for a holonomic mobile robot.The configured naviga...In this paper,a comparative study of the path planning problem using evolutionary algorithms,in comparison with classical methods such as the A*algorithm,is presented for a holonomic mobile robot.The configured navigation system,which consists of the integration of sensors sources,map formatting,global and local path planners,and the base controller,aims to enable the robot to follow the shortest smooth path delicately.Grid-based mapping is used for scoring paths efficiently,allowing the determination of collision-free trajectories from the initial to the target position.This work considers the evolutionary algorithms,the mutated cuckoo optimization algorithm(MCOA)and the genetic algorithm(GA),as a global planner to find the shortest safe path among others.A non-uniform motion coefficient is introduced for MCOA in order to increase the performance of this algorithm.A series of experiments are accomplished and analyzed to confirm the performance of the global planner implemented on a holonomic mobile robot.The results of the experiments show the capacity of the planner framework with respect to the path planning problem under various obstacle layouts.展开更多
This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The ...This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The differential equations of motion of the system are established, and the definition of Lie symmetry for the system is given. The conditions under which a Lie symmetry can directly lead up to a generalized Lutzky conserved quantity and the form of the new conserved quantity are obtained, and 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
A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints is investigated. Nielsen equations and differential equations of motion for the holono...A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints is investigated. Nielsen equations and differential equations of motion for the holonomic mechanical system with unilateral constraints are established. The definition and the criterion of Mei symmetry for Nielsen equations in the holonomic systems with unilateral constraints under the infinitesimal transformations of Lie group are also given. The expressions of the structural equation and a type of new conserved quantity of Mei symmetry for Nielsen equations in the holonomic system with unilateral constraints are obtained. An example is given to illustrate the application of the results.展开更多
Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degr...Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.展开更多
Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants, i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanica...Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants, i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results.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
Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are studied.The exact invariants induced directly from the Lie symmetry...Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are studied.The exact invariants induced directly from the Lie symmetryof the system without perturbation are given.The perturbation to the Lie symmetry is discussed and the adiabaticinvariants that have the different form from that in[Act.Phys.Sin.55(2006)3236(in Chinese)]of the perturbedsystem,are obtained.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
文摘Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was determined. Results and Conclusion The equations a Lie algebraic structure if any nonpotential generalized force doesn't exist while while the equations possess a Lie-admissible algebraic structure if nonpotential generalized forces exist .
基金Supported by National Natural Science Foundation of China(11171291)Specialized Research Fund for the Doctoral Program of Higher Education(20123250110005)Graduate Student Research and Innovation Program of Jiangsu Province(CXZZ1 0889)
文摘In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)the Fund for Fundamental Research of Beijing Institute of Technology (Grant No 20070742005)
文摘This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant No10772025)the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China (Grant No 08KJB130002)
文摘This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of the holonomic system. Some examples are given to illustrate the application of the results.
基金国家自然科学基金，湖南省自然科学基金，the Scientific Research Foundation of Education Burean of Hunan Province
文摘For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and 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 10572021 and 10372053）, and the Fundamental Research Foundation of Beijing Institute of Technology （BIT-UBF-200507A4206）.
文摘In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.
基金Supported by the National Natural Science Foundation of China under Grant No.10572021the Preparatory Research Foundation of Jiangnan University under Grant No.2008LYY011
文摘Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.
文摘For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of tile theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and qs. An example is given to illustrate the application of the results.
文摘In this paper,a comparative study of the path planning problem using evolutionary algorithms,in comparison with classical methods such as the A*algorithm,is presented for a holonomic mobile robot.The configured navigation system,which consists of the integration of sensors sources,map formatting,global and local path planners,and the base controller,aims to enable the robot to follow the shortest smooth path delicately.Grid-based mapping is used for scoring paths efficiently,allowing the determination of collision-free trajectories from the initial to the target position.This work considers the evolutionary algorithms,the mutated cuckoo optimization algorithm(MCOA)and the genetic algorithm(GA),as a global planner to find the shortest safe path among others.A non-uniform motion coefficient is introduced for MCOA in order to increase the performance of this algorithm.A series of experiments are accomplished and analyzed to confirm the performance of the global planner implemented on a holonomic mobile robot.The results of the experiments show the capacity of the planner framework with respect to the path planning problem under various obstacle layouts.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272021 and the Natural Science Foundation of High Education Department of Jiangsu Province under Grant No. 04KJA130135
文摘This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The differential equations of motion of the system are established, and the definition of Lie symmetry for the system is given. The conditions under which a Lie symmetry can directly lead up to a generalized Lutzky conserved quantity and the form of the new conserved quantity are obtained, and 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Project supported by the National Natural Science Foundation of China(Grant Nos.11142014 and 61178032)the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province of China(Grant No.CSLX12_0720)
文摘A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints is investigated. Nielsen equations and differential equations of motion for the holonomic mechanical system with unilateral constraints are established. The definition and the criterion of Mei symmetry for Nielsen equations in the holonomic systems with unilateral constraints under the infinitesimal transformations of Lie group are also given. The expressions of the structural equation and a type of new conserved quantity of Mei symmetry for Nielsen equations in the holonomic system with unilateral constraints are obtained. An example is given to illustrate the application of the results.
基金supported by China Scholarship Council (201504980073) for Zeguo Wang to visit Umea University
文摘Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.
基金Project supported by the National Natural Science Foundation of China (Grant No 10372053)
文摘Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants, i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results.
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Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are studied.The exact invariants induced directly from the Lie symmetryof the system without perturbation are given.The perturbation to the Lie symmetry is discussed and the adiabaticinvariants that have the different form from that in[Act.Phys.Sin.55(2006)3236(in Chinese)]of the perturbedsystem,are obtained.
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.
