Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation a...Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.展开更多
Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive for...Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation.These equations are highly versatile and completely compatible with Biot's wave equations for the special case of fully saturated soils.The governing equations in Cartesian coordinates are firstly transformed into a group of state differential equations by introducing the state vector.Then the transfer matrix for layered media are derived by means of a double Fourier transform.Using the transfer matrix followed by boundary and continuity conditions between strata,solutions of steady-state dynamic response for multi-layered unsaturated soils are obtained.Numerical examples show that the echoes generated by boundary and stratum interfaces make the displacement amplitude of the ground surface fluctuate with distance;the relative position of soft and hard strata has a significant influence on displacement.展开更多
An adaptive PBC strategy for SM with a time-varying load torque to track fluxand speed trajectories was proposed.The key point of this method was the identificationof terms,known as workless forces,which appeared in t...An adaptive PBC strategy for SM with a time-varying load torque to track fluxand speed trajectories was proposed.The key point of this method was the identificationof terms,known as workless forces,which appeared in the dynamic equations of SM buthad no effect on the energy balance equation of the closed loop.PBC,combined withadaptive control schemes,not only preserved the advantages of PBC such as nonexistenceof singularity,but also rejected the flux and speed tracking error caused by statorand rotor resistance variation.The rotor currents of SM were estimated via a state observer.This algorithm simplified the control structure and enhanced the robustness of thecontrol system.The feasibility and effectiveness were confirmed by experimental resultsbased on dSPACE.展开更多
The dynamic analysis of a one-DOF RSRRR spatial linkage mechanism, including four rotational joints R and one spherical joint S, is presented in the paper. It is assumed that friction occurs in the rotational joints, ...The dynamic analysis of a one-DOF RSRRR spatial linkage mechanism, including four rotational joints R and one spherical joint S, is presented in the paper. It is assumed that friction occurs in the rotational joints, whereas a spherical joint can be treated as an ideal one. The mechanism in the form of a closed-loop kinematic chain was divided by cut joint technique into two open-loop kinematic chains in place of the spherical joint. Joint coordinates and homogeneous transformation matrices were used to describe the geometry of the system. Equations of the chains＇ motion were derived using formalism of Lagrange equations. Cut joint constraints and reaction forces, acting in the cutting place---i.e, in the spherical joint, have been introduced to complete the equations of motion. As a consequence, a set of differential-algebraic equations has been obtained. In order to solve these equations, a procedure based on differentiation twice of the formulated constraint equations with respect to time has been applied. In order to determine values of friction torques in the rotational joints in each integrating step of the equations of motion, joint forces and torques were calculated using the recursive Newton-Euler algorithm taken from robotics. For the requirements of the method, a model of a rotational joint has been developed. Some examples of results of the numerical calculations made have been presented in the conclusions of the paper.展开更多
We derive the solvability conditions and an expression of the general solution to the system of matrix equations A 1X=C1 , A2Y=C2 , YB2=D2 , Y=Y*, A3Z=C3 , ZB3=D3 , Z=Z*, B4X+(B4X)+C4YC4*+D4ZD4*=A4 . Moreover, we inve...We derive the solvability conditions and an expression of the general solution to the system of matrix equations A 1X=C1 , A2Y=C2 , YB2=D2 , Y=Y*, A3Z=C3 , ZB3=D3 , Z=Z*, B4X+(B4X)+C4YC4*+D4ZD4*=A4 . Moreover, we investigate the maximal and minimal ranks and inertias of Y and Z in the above system of matrix equations. As a special case of the results, we solve the problem proposed in Farid, Moslehian, Wang and Wu's recent paper (Farid F O, Moslehian M S, Wang Q W, et al. On the Hermitian solutions to a system of adjointable operator equations. Linear Algebra Appl, 2012, 437: 1854-1891).展开更多
文摘Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.
基金National Natural Science Foundation of China(No.10272046)
文摘Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation.These equations are highly versatile and completely compatible with Biot's wave equations for the special case of fully saturated soils.The governing equations in Cartesian coordinates are firstly transformed into a group of state differential equations by introducing the state vector.Then the transfer matrix for layered media are derived by means of a double Fourier transform.Using the transfer matrix followed by boundary and continuity conditions between strata,solutions of steady-state dynamic response for multi-layered unsaturated soils are obtained.Numerical examples show that the echoes generated by boundary and stratum interfaces make the displacement amplitude of the ground surface fluctuate with distance;the relative position of soft and hard strata has a significant influence on displacement.
基金Supported by the National Basic Research Program of China(973 Program)(2005CB221505)the Special Scientific Research Foundation for Doctoral Subject of Colleges and Universities in China(20050248058)
文摘An adaptive PBC strategy for SM with a time-varying load torque to track fluxand speed trajectories was proposed.The key point of this method was the identificationof terms,known as workless forces,which appeared in the dynamic equations of SM buthad no effect on the energy balance equation of the closed loop.PBC,combined withadaptive control schemes,not only preserved the advantages of PBC such as nonexistenceof singularity,but also rejected the flux and speed tracking error caused by statorand rotor resistance variation.The rotor currents of SM were estimated via a state observer.This algorithm simplified the control structure and enhanced the robustness of thecontrol system.The feasibility and effectiveness were confirmed by experimental resultsbased on dSPACE.
文摘The dynamic analysis of a one-DOF RSRRR spatial linkage mechanism, including four rotational joints R and one spherical joint S, is presented in the paper. It is assumed that friction occurs in the rotational joints, whereas a spherical joint can be treated as an ideal one. The mechanism in the form of a closed-loop kinematic chain was divided by cut joint technique into two open-loop kinematic chains in place of the spherical joint. Joint coordinates and homogeneous transformation matrices were used to describe the geometry of the system. Equations of the chains＇ motion were derived using formalism of Lagrange equations. Cut joint constraints and reaction forces, acting in the cutting place---i.e, in the spherical joint, have been introduced to complete the equations of motion. As a consequence, a set of differential-algebraic equations has been obtained. In order to solve these equations, a procedure based on differentiation twice of the formulated constraint equations with respect to time has been applied. In order to determine values of friction torques in the rotational joints in each integrating step of the equations of motion, joint forces and torques were calculated using the recursive Newton-Euler algorithm taken from robotics. For the requirements of the method, a model of a rotational joint has been developed. Some examples of results of the numerical calculations made have been presented in the conclusions of the paper.
基金National Natural Science Foundation of China (Grant No. 11171205)Natural Science Foundation of Shanghai (Grant No. 11ZR1412500)+2 种基金the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093108110001)Shanghai Leading Academic Discipline Project (Grant No. J50101)Innovation Foundation of Shanghai University (Grant No. SHUCX120109)
文摘We derive the solvability conditions and an expression of the general solution to the system of matrix equations A 1X=C1 , A2Y=C2 , YB2=D2 , Y=Y*, A3Z=C3 , ZB3=D3 , Z=Z*, B4X+(B4X)+C4YC4*+D4ZD4*=A4 . Moreover, we investigate the maximal and minimal ranks and inertias of Y and Z in the above system of matrix equations. As a special case of the results, we solve the problem proposed in Farid, Moslehian, Wang and Wu's recent paper (Farid F O, Moslehian M S, Wang Q W, et al. On the Hermitian solutions to a system of adjointable operator equations. Linear Algebra Appl, 2012, 437: 1854-1891).
