In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of cl...In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.展开更多
The new sustainable tillage system needs new machines which are the combination of well accepted disc harrow and cultivator or chisel/ripper. To find the type of ripper shank we have done a research program with 7 dif...The new sustainable tillage system needs new machines which are the combination of well accepted disc harrow and cultivator or chisel/ripper. To find the type of ripper shank we have done a research program with 7 different shape and size tools. The geometrical parameters were determined in laboratory, the performance （loosening effect, depth etc） and draft requirements were measured on loamy soil stubble field （the speed range： 2.5-7.5 krrdh）. Developing a combined evaluation system-based on performance and draft data-to select the most favorable shank type for our condition was found one which has the following features： the size of the point： rake angle = 25°, length = 240 mm, width = 80mm; the equation of the shank curve： y = axb, where a = 2-3.5 and b = 0.04-0.05.展开更多
A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear tran...A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.展开更多
A new motion planning method is proposed for enlarging the solvable space of zero-disturbance motion planning for the space free-floating manipulator system. First, a class of translational zero-disturbance curves is ...A new motion planning method is proposed for enlarging the solvable space of zero-disturbance motion planning for the space free-floating manipulator system. First, a class of translational zero-disturbance curves is put forward for the first time. The equation of translational zero-disturbance curve is deduced using the nonholonomic constraint of the manipulator system, and its characteristics are also discussed. Second, the zero-disturbance curve of the whole operating process is divided into two segments. The first one is a translational zero-disturbance curve which passes through the target point. Another one is a common zero-disturbance curve which passes through the original point and intersects with the translational zero-disturbance curve. Finally, the common zero-disturbance curve is obtained by a hybrid programming strategy based on Gauss pseudo-spectral method (GPM) and direct shooting method (DSM). The numerical simulation results indicate that the proposed method is effective, and that the solvable space of this method almost covers the whole work space of the manipulator system.展开更多
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an appl...For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.展开更多
This paper concerns a system of nonlinear wave equations describing the vibra- tions of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibr...This paper concerns a system of nonlinear wave equations describing the vibra- tions of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions, and, by using the methods of quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundary value problem has classical solutions existing in neighborhoods of the ＂stretched＂ equilibrium solutions. Then the local controllability of such networks near such equilib- rium configurations in a certain specified time interval is proved. Finally, it is proved that, given two different equilibrium states satisfying certain conditions, it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval.展开更多
文摘In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.
文摘The new sustainable tillage system needs new machines which are the combination of well accepted disc harrow and cultivator or chisel/ripper. To find the type of ripper shank we have done a research program with 7 different shape and size tools. The geometrical parameters were determined in laboratory, the performance （loosening effect, depth etc） and draft requirements were measured on loamy soil stubble field （the speed range： 2.5-7.5 krrdh）. Developing a combined evaluation system-based on performance and draft data-to select the most favorable shank type for our condition was found one which has the following features： the size of the point： rake angle = 25°, length = 240 mm, width = 80mm; the equation of the shank curve： y = axb, where a = 2-3.5 and b = 0.04-0.05.
文摘A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.
文摘A new motion planning method is proposed for enlarging the solvable space of zero-disturbance motion planning for the space free-floating manipulator system. First, a class of translational zero-disturbance curves is put forward for the first time. The equation of translational zero-disturbance curve is deduced using the nonholonomic constraint of the manipulator system, and its characteristics are also discussed. Second, the zero-disturbance curve of the whole operating process is divided into two segments. The first one is a translational zero-disturbance curve which passes through the target point. Another one is a common zero-disturbance curve which passes through the original point and intersects with the translational zero-disturbance curve. Finally, the common zero-disturbance curve is obtained by a hybrid programming strategy based on Gauss pseudo-spectral method (GPM) and direct shooting method (DSM). The numerical simulation results indicate that the proposed method is effective, and that the solvable space of this method almost covers the whole work space of the manipulator system.
基金Project supported by the Special Funds forMajor State Basic Research Projects ofChina.
文摘For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
基金supported by the DFG SPP1253:Optimization with PDE-Constaintsthe DFG-CE315 Cluster of Excellence:Engineering of Advanced Materials
文摘This paper concerns a system of nonlinear wave equations describing the vibra- tions of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions, and, by using the methods of quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundary value problem has classical solutions existing in neighborhoods of the ＂stretched＂ equilibrium solutions. Then the local controllability of such networks near such equilib- rium configurations in a certain specified time interval is proved. Finally, it is proved that, given two different equilibrium states satisfying certain conditions, it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval.
