The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics were considered. A new algorithm was presented for solving constraints based on Wu elimination method. The new alg...The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics were considered. A new algorithm was presented for solving constraints based on Wu elimination method. The new algorithm does not need to calculate the rank of Hessian matrix and determine the linear dependence of equations, so the steps of calculation decrease greatly. In addition, the expanding of expression occurring in the computing process is smaller. Using the symbolic computation software platform, the new algorithm can be executed in computers.展开更多
The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics,which serves as a powerful instrument in finding saddle points and constructing the solution la...The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics,which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems on the high-dimensional sphere.Due to the semi-implicit treatment and the novel computational procedure,the orthonormality of numerical solutions at each time step could not be fully employed to simplify the derivations,and the computations of the state variable and directional vectors are coupled with the retraction,the vector transport and the orthonormalization procedure,which significantly complicates the analysis.They address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.展开更多
A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynami...A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.展开更多
Energy system structures are evolving toward increasing cost benefits,efficiency,and environmental sustainability.Achieving these goals is contingent upon the utilization of renewables.Energy storage is the primary ch...Energy system structures are evolving toward increasing cost benefits,efficiency,and environmental sustainability.Achieving these goals is contingent upon the utilization of renewables.Energy storage is the primary challenge associated with renewable energy.Hydrogen and fuel cells are key in addressing these issues.Iran demonstrates significant renewable-energy potential;however,only a small fraction of this potential is currently utilized.Furthermore,the country’s energy system is inefficient.Thus,a feasible plan for creating a sustainable energy system that reliably includes renewables must be developed.The household heating and cooling system is a good starting point.The required model must be dynamic and consider climatic effects,which have not been sufficiently addressed in previous studies conducted in Iran.In this study,the optimal thermodynamic variables,output power,and waste heat for different fuel-cell capacities are first determined by solving a nonlinear model.Subsequently,through a dynamic multicriteria optimization of household heating–cooling systems,the optimal system configurations for 10 years across five different case studies in various climates in Iran are determined.The objective function is to minimize the total costs,which include technology,energy,raw material,and social costs.This study demonstrates the feasibility of developing a fuel-cell technology to satisfy the energy demands of household heating and cooling systems based on case studies.However,reusing waste heat is only practical in hot and humid climates because of the low heating demand.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10401021)the Scientific Research Foundation of Graduate University of Chinese Academy of Sciences
文摘The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics were considered. A new algorithm was presented for solving constraints based on Wu elimination method. The new algorithm does not need to calculate the rank of Hessian matrix and determine the linear dependence of equations, so the steps of calculation decrease greatly. In addition, the expanding of expression occurring in the computing process is smaller. Using the symbolic computation software platform, the new algorithm can be executed in computers.
基金supported by the National Natural Science Foundation of China(Nos.12225102,12050002,12288101,12301555)the National Key R&D Program of China(No.2021YFF1200500)the Taishan Scholars Program of Shandong Province。
文摘The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics,which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems on the high-dimensional sphere.Due to the semi-implicit treatment and the novel computational procedure,the orthonormality of numerical solutions at each time step could not be fully employed to simplify the derivations,and the computations of the state variable and directional vectors are coupled with the retraction,the vector transport and the orthonormalization procedure,which significantly complicates the analysis.They address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.
文摘A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.
文摘Energy system structures are evolving toward increasing cost benefits,efficiency,and environmental sustainability.Achieving these goals is contingent upon the utilization of renewables.Energy storage is the primary challenge associated with renewable energy.Hydrogen and fuel cells are key in addressing these issues.Iran demonstrates significant renewable-energy potential;however,only a small fraction of this potential is currently utilized.Furthermore,the country’s energy system is inefficient.Thus,a feasible plan for creating a sustainable energy system that reliably includes renewables must be developed.The household heating and cooling system is a good starting point.The required model must be dynamic and consider climatic effects,which have not been sufficiently addressed in previous studies conducted in Iran.In this study,the optimal thermodynamic variables,output power,and waste heat for different fuel-cell capacities are first determined by solving a nonlinear model.Subsequently,through a dynamic multicriteria optimization of household heating–cooling systems,the optimal system configurations for 10 years across five different case studies in various climates in Iran are determined.The objective function is to minimize the total costs,which include technology,energy,raw material,and social costs.This study demonstrates the feasibility of developing a fuel-cell technology to satisfy the energy demands of household heating and cooling systems based on case studies.However,reusing waste heat is only practical in hot and humid climates because of the low heating demand.
