Let M(2)be the group of rigid motions of the plane.The Fourier transform and the Piancherel formula on M(2)can be explicitly given by the general group representation theory.Using this fact.we establish a kind of unce...Let M(2)be the group of rigid motions of the plane.The Fourier transform and the Piancherel formula on M(2)can be explicitly given by the general group representation theory.Using this fact.we establish a kind of uncertainty principle on M(2).The result can easily be generalized to higher dimensional cases.An application of the result yields an uncertainty principle on the Euclidean spaces obtained by R.S.Strichartz.展开更多
A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an a...A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.展开更多
Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformat...Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformation models, neglecting the biomechanical differences between rigid structures and soft tissues, which compromises registration accuracy, especially during significant bone displacements. Method To address this issue, we introduce RE-Reg, a rigid-elastic CT-CBCT image registration framework that jointly learns rigid bone motion and soft tissue deformation. RE-Reg incorporates a rigid alignment(RA) module to estimate global bone motion and an elastic deformation(ED) module to model soft tissue deformation, preserving bony structures through bone shape preservation(BSP) loss. Result Our comprehensive evaluation on publicly available datasets demonstrates that RE-Reg significantly outperforms existing methods in terms of registration accuracy and rigid bone structure preservation, achieving a 1.3% improvement in Dice similarity coefficient(DSC) and a 23% reduction in rigid bone deformation(%Δvol) compared with the best baseline. Conclusion This framework not only enhances anatomical fidelity but also ensures biomechanical plausibility and provides a valuable tool for image-guided orthopedic surgery. This code is available athttps://github.com/Zq-Huang/RE-Reg.展开更多
In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and s...In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean C^(2)-smooth curves on surfaces.We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.展开更多
An open-plus-closed-loop （OPCL） control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitationM force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body sup...An open-plus-closed-loop （OPCL） control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitationM force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler＇s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts： the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.展开更多
Recognizing and reproducing spatiotemporal motions are necessary when analyzing behaviors andmovements during human-robot interaction. Rigid body motion trajectories are proven as compact and informativeclues in chara...Recognizing and reproducing spatiotemporal motions are necessary when analyzing behaviors andmovements during human-robot interaction. Rigid body motion trajectories are proven as compact and informativeclues in characterizing motions. A flexible dual square-root function (DSRF) descriptor for representing rigid bodymotion trajectories, which can offer robustness in the description over raw data, was proposed in our previousstudy. However, this study focuses on exploring the application of the DSRF descriptor for effective backwardmotion reproduction and motion recognition. Specifically, two DSRF-based reproduction methods are initiallyproposed, including the recursive reconstruction and online optimization. New trajectories with novel situationsand contextual information can be reproduced from a single demonstration while preserving the similarities withthe original demonstration. Furthermore, motion recognition based on DSRF descriptor can be achieved byemploying a template matching method. Finally, the experimental results demonstrate the effectiveness of theproposed method for rigid body motion reproduction and recognition.展开更多
In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a R...In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary;globally.under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary展开更多
In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned man...In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.展开更多
A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerica...A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall, viscosity ratios, combined surface tension and buoyancy parameters and ambient flow parameters. Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes. When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances. When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes. In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow, buoyancy and the stronger wall action to the flow. The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis, which increases when the initial stand-off distance increases. When the initial stand-off distance increases the stress induced by drop motion decreases substantially. The surface tension effects resist the deformation and smooth the profile of the drop surfaces. The drop viscosity will reduce the deformation and migration of the drop.展开更多
The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the...The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.展开更多
A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We desc...A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We describe an algorithm to robustly predict futuristic configurations of a moving target in a time-varying environment. We use the Kalman filter for tracking and motion prediction purposes because it is a very effective and useful estimator. It implements a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance. The target motion is unconstrained. The proposed algorithm may be viewed as a seed for a range of applications, one of which is robot motion planning in a time-changing environment. A significant feature of the proposed algorithm (when compared to similar ones) is its ability to embark the prediction process from the first time step;no need to wait for few time steps as in the autoregressive-based systems. Simulation results supports our claims and demonstrate the superiority of the proposed model.展开更多
The control problem of coordinated motion of a free-floating space rigid manipulator with external disturbance is discussed. By combining linear momentum conversion and the Lagrangian approach, the full-control dynami...The control problem of coordinated motion of a free-floating space rigid manipulator with external disturbance is discussed. By combining linear momentum conversion and the Lagrangian approach, the full-control dynamic equation and the Jacobian relation of a free-floating space rigid manipulator are established and then inverted to the state equation for control design. Based on the terminal sliding mode control （SMC） technique, a mathematical expression of the terminal sliding surface is proposed. The terminal SMC scheme is then developed for coordinated motion between the base＇s attitude and the end-effector of the free-floating space manipulator with external disturbance. This proposed control scheme not only guarantees the existence of the sliding phase of the closed-loop system, but also ensures that the output tracking error converges to zero in finite time. In addition, because the initial system state is always at the terminal sliding surface, the control scheme can eliminate reaching phase of the SMC and guarantee global robustness and stability of the closed-loop system. A planar free-floating space rigid manipulator is simulated to verify the feasibility of the proposed control scheme.展开更多
An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors...An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.展开更多
Rigid ellipsoidal objects(gravels and porphyroclasts)in ductile zone is an important factor to indicate the kinematics and dynamics.Jeffery’s theory(Jeffery G,1922),a quantitative research method,for the rotation oft...Rigid ellipsoidal objects(gravels and porphyroclasts)in ductile zone is an important factor to indicate the kinematics and dynamics.Jeffery’s theory(Jeffery G,1922),a quantitative research method,for the rotation ofthe rigid objects(no deformation)in the Newtonian fluid of the simple deformation field has been widely applied by geologists to the study of fabrics in rocks.The theory展开更多
Considering rigid-liquid-flexible coupling effect, dynamic formulation for a two-dimensional rectangular tank with liquid sloshing connected to a flexible beam is proposed. Differing from the traditional formulation w...Considering rigid-liquid-flexible coupling effect, dynamic formulation for a two-dimensional rectangular tank with liquid sloshing connected to a flexible beam is proposed. Differing from the traditional formulation which considered either the rotational motion or the translational motion of the tank, this formulation can be applied for rigid-liquid-flexible coupling dynamic analysis of tank undergoing translational and rotational motion based on the theorem of momentum and the theorem of moment of momentum. Furthermore, stiffening terms are included in the dynamics equations of the flexible beam. Firstly, the dynamic equations of the rigid-liquid coupling system and the flexible beam are derived, respectively, and then by introducing the Lagrange-multipliers,the rigid-liquid-flexible coupling equations can be combined with acceleration constraint equations. Finally, the mix differential-algebraic equations are solved to investigate the rigid-liquid-flexible coupling dynamic performance of the system.展开更多
In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint...In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint. A general kinematic model of the space robot was established based on the law of linear and angular momentum conservation. A combinational joint model was established combined with bionic joint and closed motion. The attitude transformation of planar,two DOF and three DOF is analyzed and simulated by the model,and it is verified that the feasibility of attitude transformation in three DOF space. Finally,the specific scheme of disturbance elimination in attitude transformation is presented and simulation results are obtained.Therefore,the range of application field of the bionic joint model has been expanded.展开更多
The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the ide...The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.展开更多
Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of fail...Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.展开更多
文摘Let M(2)be the group of rigid motions of the plane.The Fourier transform and the Piancherel formula on M(2)can be explicitly given by the general group representation theory.Using this fact.we establish a kind of uncertainty principle on M(2).The result can easily be generalized to higher dimensional cases.An application of the result yields an uncertainty principle on the Euclidean spaces obtained by R.S.Strichartz.
文摘A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.
基金Supported by the National Natural Science Foundation of China(Grant Nos.62025104,62331005,and U22A2052)the Beijing Natural Science Foundation(Grant No.L242100).
文摘Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformation models, neglecting the biomechanical differences between rigid structures and soft tissues, which compromises registration accuracy, especially during significant bone displacements. Method To address this issue, we introduce RE-Reg, a rigid-elastic CT-CBCT image registration framework that jointly learns rigid bone motion and soft tissue deformation. RE-Reg incorporates a rigid alignment(RA) module to estimate global bone motion and an elastic deformation(ED) module to model soft tissue deformation, preserving bony structures through bone shape preservation(BSP) loss. Result Our comprehensive evaluation on publicly available datasets demonstrates that RE-Reg significantly outperforms existing methods in terms of registration accuracy and rigid bone structure preservation, achieving a 1.3% improvement in Dice similarity coefficient(DSC) and a 23% reduction in rigid bone deformation(%Δvol) compared with the best baseline. Conclusion This framework not only enhances anatomical fidelity but also ensures biomechanical plausibility and provides a valuable tool for image-guided orthopedic surgery. This code is available athttps://github.com/Zq-Huang/RE-Reg.
基金supported by National Natural Science Foundation of China(Grant No.11771070)。
文摘In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean C^(2)-smooth curves on surfaces.We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.
基金supported by the National Natural Science Foundation of China(No.11072038)the Municipal Key Programs of Natural Science Foundation of Beijing(No.KZ201110772039)
文摘An open-plus-closed-loop （OPCL） control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitationM force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler＇s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts： the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.
基金the Science and Technology Commission of Shanghai Municipality(No.20DZ2220400)the Interdisciplinary Program of Shanghai Jiao Tong University(No.YG2021QN117)。
文摘Recognizing and reproducing spatiotemporal motions are necessary when analyzing behaviors andmovements during human-robot interaction. Rigid body motion trajectories are proven as compact and informativeclues in characterizing motions. A flexible dual square-root function (DSRF) descriptor for representing rigid bodymotion trajectories, which can offer robustness in the description over raw data, was proposed in our previousstudy. However, this study focuses on exploring the application of the DSRF descriptor for effective backwardmotion reproduction and motion recognition. Specifically, two DSRF-based reproduction methods are initiallyproposed, including the recursive reconstruction and online optimization. New trajectories with novel situationsand contextual information can be reproduced from a single demonstration while preserving the similarities withthe original demonstration. Furthermore, motion recognition based on DSRF descriptor can be achieved byemploying a template matching method. Finally, the experimental results demonstrate the effectiveness of theproposed method for rigid body motion reproduction and recognition.
文摘In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary;globally.under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary
基金sponsored by Bureau Veritas under the administration of Dr.ime Malenica
文摘In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.
基金Project supported by the National Natural Science Foundation of China (No. 10272032)
文摘A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall, viscosity ratios, combined surface tension and buoyancy parameters and ambient flow parameters. Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes. When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances. When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes. In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow, buoyancy and the stronger wall action to the flow. The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis, which increases when the initial stand-off distance increases. When the initial stand-off distance increases the stress induced by drop motion decreases substantially. The surface tension effects resist the deformation and smooth the profile of the drop surfaces. The drop viscosity will reduce the deformation and migration of the drop.
文摘The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.
文摘A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We describe an algorithm to robustly predict futuristic configurations of a moving target in a time-varying environment. We use the Kalman filter for tracking and motion prediction purposes because it is a very effective and useful estimator. It implements a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance. The target motion is unconstrained. The proposed algorithm may be viewed as a seed for a range of applications, one of which is robot motion planning in a time-changing environment. A significant feature of the proposed algorithm (when compared to similar ones) is its ability to embark the prediction process from the first time step;no need to wait for few time steps as in the autoregressive-based systems. Simulation results supports our claims and demonstrate the superiority of the proposed model.
基金the National Natural Science Foundation of China(Nos.10672040 and 10372022)the Natural Science Foundation of Fujian Province,China(No.E0410008)
文摘The control problem of coordinated motion of a free-floating space rigid manipulator with external disturbance is discussed. By combining linear momentum conversion and the Lagrangian approach, the full-control dynamic equation and the Jacobian relation of a free-floating space rigid manipulator are established and then inverted to the state equation for control design. Based on the terminal sliding mode control （SMC） technique, a mathematical expression of the terminal sliding surface is proposed. The terminal SMC scheme is then developed for coordinated motion between the base＇s attitude and the end-effector of the free-floating space manipulator with external disturbance. This proposed control scheme not only guarantees the existence of the sliding phase of the closed-loop system, but also ensures that the output tracking error converges to zero in finite time. In addition, because the initial system state is always at the terminal sliding surface, the control scheme can eliminate reaching phase of the SMC and guarantee global robustness and stability of the closed-loop system. A planar free-floating space rigid manipulator is simulated to verify the feasibility of the proposed control scheme.
基金Project supported by the National Natural Science Foundation of China (No. 10372014).
文摘An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.
文摘Rigid ellipsoidal objects(gravels and porphyroclasts)in ductile zone is an important factor to indicate the kinematics and dynamics.Jeffery’s theory(Jeffery G,1922),a quantitative research method,for the rotation ofthe rigid objects(no deformation)in the Newtonian fluid of the simple deformation field has been widely applied by geologists to the study of fabrics in rocks.The theory
基金the National Natural Science Foundation of China(Nos.11272203 and 11132007)
文摘Considering rigid-liquid-flexible coupling effect, dynamic formulation for a two-dimensional rectangular tank with liquid sloshing connected to a flexible beam is proposed. Differing from the traditional formulation which considered either the rotational motion or the translational motion of the tank, this formulation can be applied for rigid-liquid-flexible coupling dynamic analysis of tank undergoing translational and rotational motion based on the theorem of momentum and the theorem of moment of momentum. Furthermore, stiffening terms are included in the dynamics equations of the flexible beam. Firstly, the dynamic equations of the rigid-liquid coupling system and the flexible beam are derived, respectively, and then by introducing the Lagrange-multipliers,the rigid-liquid-flexible coupling equations can be combined with acceleration constraint equations. Finally, the mix differential-algebraic equations are solved to investigate the rigid-liquid-flexible coupling dynamic performance of the system.
文摘In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint. A general kinematic model of the space robot was established based on the law of linear and angular momentum conservation. A combinational joint model was established combined with bionic joint and closed motion. The attitude transformation of planar,two DOF and three DOF is analyzed and simulated by the model,and it is verified that the feasibility of attitude transformation in three DOF space. Finally,the specific scheme of disturbance elimination in attitude transformation is presented and simulation results are obtained.Therefore,the range of application field of the bionic joint model has been expanded.
文摘The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.
文摘Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.
