Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretizati...Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretization; Details on the numerical tests.展开更多
In this paper,we study the dynamics of an idealized benchmark bicycle moving on a surface of revolution.We employ symbolic manipulations to derive the contact constraint equations from an ordered process,and apply the...In this paper,we study the dynamics of an idealized benchmark bicycle moving on a surface of revolution.We employ symbolic manipulations to derive the contact constraint equations from an ordered process,and apply the Lagrangian equations of the first type to establish the nonlinear differential algebraic equations(DAEs),leaving nine coupled differential equations,six contact equations,two holonomic constraint equations and four nonholonomic constraint equations.We then present a complete description of hands-free circular motions,in which the time-dependent variables are eliminated through a rotation transformation.We find that the circular motions,similar to those of the bicycle moving on a horizontal surface,nominally fall into four solution families,characterized by four curves varying with the angular speed of the front wheel.Then,we numerically investigate how the topological profiles of these curves change with the parameter of the revolution surface.Furthermore,we directly linearize the nonlinear DAEs,from which a reduced linearized system is obtained by removing the dependent coordinates and counting the symmetries arising from cyclic coordinates.The stability of the circular motion is then analyzed according to the eigenvalues of the Jacobian matrix of the reduced linearized system around the equilibrium position.We find that a stable circular motion exists only if the curvature of the revolution surface is very small and it is limited in small sections of solution families.Finally,based on the numerical simulation of the original nonlinear DAEs system,we show that the stable circular motion is not asymptotically stable.展开更多
The simulation of a high-temperature gas-cooled reactor pebble-bed module(HTR-PM) plant is discussed.This lumped parameter model has the form of a set differential algebraic equations(DAEs) that include stiff equation...The simulation of a high-temperature gas-cooled reactor pebble-bed module(HTR-PM) plant is discussed.This lumped parameter model has the form of a set differential algebraic equations(DAEs) that include stiff equations to model point neutron kinetics.The nested approach is the most common method to solve DAE,but this approach is very expensive and time-consuming due to inner iterations.This paper deals with an alternative approach in which a simultaneous solution method is used.The DAEs are discretized over a time horizon using collocation on finite elements,and Radau collocation points are applied.The resulting nonlinear algebraic equations can be solved by existing solvers.The discrete algorithm is discussed in detail;both accuracy and stability issues are considered.Finally,the simulation results are presented to validate the efficiency and accuracy of the simultaneous approach that takes much less time than the nested one.展开更多
文摘Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretization; Details on the numerical tests.
基金National Natural Science Foundation of China(Grants 11932001 and 11702002).
文摘In this paper,we study the dynamics of an idealized benchmark bicycle moving on a surface of revolution.We employ symbolic manipulations to derive the contact constraint equations from an ordered process,and apply the Lagrangian equations of the first type to establish the nonlinear differential algebraic equations(DAEs),leaving nine coupled differential equations,six contact equations,two holonomic constraint equations and four nonholonomic constraint equations.We then present a complete description of hands-free circular motions,in which the time-dependent variables are eliminated through a rotation transformation.We find that the circular motions,similar to those of the bicycle moving on a horizontal surface,nominally fall into four solution families,characterized by four curves varying with the angular speed of the front wheel.Then,we numerically investigate how the topological profiles of these curves change with the parameter of the revolution surface.Furthermore,we directly linearize the nonlinear DAEs,from which a reduced linearized system is obtained by removing the dependent coordinates and counting the symmetries arising from cyclic coordinates.The stability of the circular motion is then analyzed according to the eigenvalues of the Jacobian matrix of the reduced linearized system around the equilibrium position.We find that a stable circular motion exists only if the curvature of the revolution surface is very small and it is limited in small sections of solution families.Finally,based on the numerical simulation of the original nonlinear DAEs system,we show that the stable circular motion is not asymptotically stable.
基金Project supported by the National Basic Research Program of China (No. 2009CB320603)the National Natural Science Foundation of China (Nos. 60974007 and 60934007)
文摘The simulation of a high-temperature gas-cooled reactor pebble-bed module(HTR-PM) plant is discussed.This lumped parameter model has the form of a set differential algebraic equations(DAEs) that include stiff equations to model point neutron kinetics.The nested approach is the most common method to solve DAE,but this approach is very expensive and time-consuming due to inner iterations.This paper deals with an alternative approach in which a simultaneous solution method is used.The DAEs are discretized over a time horizon using collocation on finite elements,and Radau collocation points are applied.The resulting nonlinear algebraic equations can be solved by existing solvers.The discrete algorithm is discussed in detail;both accuracy and stability issues are considered.Finally,the simulation results are presented to validate the efficiency and accuracy of the simultaneous approach that takes much less time than the nested one.
