By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integra...By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integral. The effect of noncanonical strength, off-axis distance and vortex sign on spatial correlation singularities in far field is stressed. Furthermore, far-field OAM spectra and densities are also investigated, and the OAM detection and crosstalk probabilities are discussed. The results show that the number of dislocations of SCS always equals the sum of absolute values of topological charges for canonical or noncanonical vortex pairs. Although the sum of the product of each OAM mode and its power weight equals the algebraic sum of topological charges for canonical vortex pairs, the relationship no longer holds in the noncanonical case except for opposite-charge vortex pairs. The changes of off-axis distance, noncanonical strength or coherence length can lead to a more dominant power in adjacent mode than that in center detection mode, which also indicates that crosstalk probabilities of adjacent modes exceed the center detection probability. This work may provide potential applications in OAM-based optical communication, imaging, sensing and computing.展开更多
This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle av...This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle avoidance is obtained. The angular velocity is constrained by the controller, so the planned path guarantees the safety of users. According to Lyapunov theory, the controller is designed to maintain stability in terms of solutions of linear matrix inequalities and the controller's performance with safe angular velocity constraints is derived.The simulation and experiment results confirm the effectiveness of the proposed method and verify that the angular velocity of the cushion robot provided safe motion with obstacle avoidance.展开更多
Under the quadratic approximation of the Rytov＇s phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbu...Under the quadratic approximation of the Rytov＇s phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.展开更多
The performance of any inertially stabilized platform （ISP） is strongly related to the bandwidth and accuracy of the angular velocity signals. This paper discusses the development of an optimal state estimator for s...The performance of any inertially stabilized platform （ISP） is strongly related to the bandwidth and accuracy of the angular velocity signals. This paper discusses the development of an optimal state estimator for sensing inertial velocity using low-cost micro-electro-mechanical systems （MEMS） sensors. A low-bandwidth gyroscope is used alone with two low-performance accelerometers to obtain the estimation. The gyroscope has its own limited dynamics and mainly contributes to the low-frequency components of the estimation. The accelerometers have inherent biases and mainly contribute to the high-frequency components of the estimation. Extensive experimental results show that the state estimator can achieve high-performance signals over a wide range of velocities without drifts in both the t- and s-domains. Furthermore, with applications in miniature inertially stabilized platforms, the control characteristic presents a significantly improvement over the existing methods. The method can be also applied to robotics, attitude estimation, and friction compensation.展开更多
The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft.The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adapt...The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft.The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adaptive feedback control.An angular velocity feedback tracking algorithm is firstly developed based on the precisely known attitude dynamics of the spacecraft,and the global tracking of the control algorithm is proved based on the Lyapunov analysis.An adaptation mechanism is then designed to deal with the dynamic uncertainties of the spacecraft.Such an adaptation mechanism enables the controller to track any desired angular velocity trajectories even in the presence of uncertain inertia parameters,although it does not guarantee the inertia tensor being precisely identified.To verify the effectiveness of the proposed adaptive control policy,computer simulations on dynamic equations of a spacecraft are conducted and their results are discussed.展开更多
Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dy...Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.展开更多
The continuous extrusion forming process for producing large section copper concave bus bar under different extrusion wheel angular velocities was studied by three-dimensional finite element technology based on softwa...The continuous extrusion forming process for producing large section copper concave bus bar under different extrusion wheel angular velocities was studied by three-dimensional finite element technology based on software DEFORM-3D. The rigid-viscoplastic constitutive equation was employed in the model. The numerical simulation results show that the deformation body flow velocity in the die orifice increases gradually with the increase of the extrusion wheel angular velocity. But slippage between the rod and extrusion wheel occurs when the extrusion wheel angular velocity is high. The effective stress near the die orifice enhances gradually with increasing extrusion wheel angular velocity. High stress is concentrated in adjacent regions of the flash gap. The effective strain gradient is greater near the abutment than that near the die orifice. The effective strain of the product increases gradually with increasing extrusion wheel angular velocity. In the deformation process, the deformation body temperature increases remarkably due to friction and deformation. So the cooling is necessary in the region of the die and tools.展开更多
In order to constrain the crustal wave velocity structure in the southernTibetan crust and provide insight into the contribution of crustal composition, geothermal gradientand partial melting to the velocity structure...In order to constrain the crustal wave velocity structure in the southernTibetan crust and provide insight into the contribution of crustal composition, geothermal gradientand partial melting to the velocity structure, which is characterized by low average crustalvelocities and widespread presence of low-velocity zone(s), the authors model the crustal velocityand density as functions of depth corresponding to various heat flow values in light of velocitymeasurements at high temperature and high pressure. The modeled velocity and density are regarded ascomparison standards. The comparison of the standards with seismic observations in southern Tibetimplies that the predominantly felsic composition at high heat flow cannot explain the observedvelocity structure there. Hence, the authors are in favor of attributing low average crustalvelocities and low-velocity zone(s) observed in southern Tibet mainly to partial melting. Modelingbased on the experimental results suggests that a melting percentage of 7-12 could account for thelow-velocity zone(s).展开更多
In this paper,the estimator-based Global Positioning System(GPS)attitude and angular velocity determination is presented.Outputs of the attitude estimator include the attitude angles and attitude rates or body angular...In this paper,the estimator-based Global Positioning System(GPS)attitude and angular velocity determination is presented.Outputs of the attitude estimator include the attitude angles and attitude rates or body angular velocities,depending on the design of estimator.Traditionally as a position,velocity and time sensor,the GPS also offers a free attitude-determination interferometer.GPS research and applications to the field of attitude determination using carrier phase or Doppler measurement has been extensively conducted.The rawattitude solution using the interferometry technique based on the least-squares approach is inherently noisy.The estimator such as the Kalman filter(KF)or extended Kalman filter(EKF)can be incorporated into the GPS interferometer,potentially providing several advantages,such as accuracy improvement,reliability enhancement,and real-time characteristics.Three estimator-based approaches are investigated for performance comparison,including(1)KF with measurement involving attitude angles only;(2)EKF with measurements based on attitude angles only;(3)EKF with measurements involving both attitude angles and body angular rates.The assistance from body mounted gyroscopes,if available,can be utilized as the measurements for further performance improvement,especially useful for the case of signal-challenged environment,such as the GPS outages.Modeling of the dynamic process involving the body angular rates and derivation of the related algorithm will be presented.Simulation results for various estimator-based approaches are conducted;performance comparison is presented for the case of GPS outages.展开更多
The influences of die parameters on shear strain were investigated by using two-dimensional finite element simulation.New formulas of shear strain were proposed.According to the results of formulas,the shear strain sh...The influences of die parameters on shear strain were investigated by using two-dimensional finite element simulation.New formulas of shear strain were proposed.According to the results of formulas,the shear strain showed a linear dependence on the difference between internal and external fillet radius and the slope was determined by the intersection angle.The simulation results indicated that the velocities of the points from different zones were different in the specimen and the motion trajectories of different points did not follow geometrical laws.The influences of the average velocity and the motion trajectory on shear strain were incorporated in the formula to calculate the shear strain produced during equalchannel angular pressing process.The reliability of simulation results has been partially validated by experiments.展开更多
In order to find out the influence of the instability of angular velocity of the rotating carrier itself on the stability of silicon micromachined gyroscope, the digital models for relative error of the high and low d...In order to find out the influence of the instability of angular velocity of the rotating carrier itself on the stability of silicon micromachined gyroscope, the digital models for relative error of the high and low damping gyroscope's output signal are given respectively, based on the motion equations of the silicon micromachined gyroscope. Theory proves that the output signal error of the silicon micromachined sensor is mainly caused by the instability of damping factor and the angular velocity of the rotating carrier itself. The experiment result indicates that the error of proportionality coefficient of output voltage which is caused by the instability of the angular velocity of the rotating carrier itself reaches to 4.1 %. Theoretical demonstration and experimental verification show that the instability of angular velocity of the rotating carrier itself has an important effect on the stability of low damping silicon micromachined gyroscope.展开更多
The study object is the angular output velocity of the drive shaft which is made up of two series-wound cross universal joints. We have deduced the function relation between the angular output velocity and initiative ...The study object is the angular output velocity of the drive shaft which is made up of two series-wound cross universal joints. We have deduced the function relation between the angular output velocity and initiative input angle of the drive shaft with double cross universal joints that is based on the calculation formula of the angular output velocity of a single cross universal joint, and by analyzing the relation between the two input angles. By using this function relation, the constant velocity condition of the drive shaft with double cross universal joints＂ is verified. The step-by-step searching algorithm is adopted to obtain the optimal phase angle that leads to the minimum fluctuate index of the angular output velocity in the vary velocity condition. At the same time, we worked out the maximal and minimum value of the angular output velocity, and their initiative input angle. The correctness of the function of the angular output velocity and the step-by-step search algorithm are verified by an ADAMS simulation example.展开更多
We predict high-velocity magnetic domain wall(DW)motion driven by out-of-plane acoustic spin in surface acoustic waves(SAWs).We demonstrate that the SAW propagating at a 30-degree angle relative to the x-axis of a 128...We predict high-velocity magnetic domain wall(DW)motion driven by out-of-plane acoustic spin in surface acoustic waves(SAWs).We demonstrate that the SAW propagating at a 30-degree angle relative to the x-axis of a 128∘Y-LiNbO_(3) substrate exhibits uniform out-of-plane spin angular momentum.This acoustic spin triggers the DW motion at a velocity exceeding 50 m/s in a way that is similar to the spin-transfer-torque effect.This phenomenon highlights the potential of acoustic spin in enabling rapid DW displacement,offering an innovative approach to developing energy-efficient spintronic devices.展开更多
In simulation,sometimes we wish to stipulate a specified angular velocity applied to a given frame.Although position,linear velocity and orientation interpolations are well studied,less attention is paid on angular ve...In simulation,sometimes we wish to stipulate a specified angular velocity applied to a given frame.Although position,linear velocity and orientation interpolations are well studied,less attention is paid on angular velocity interpolation.In this paper,a new method to smoothly interpolate angular velocity using quaternions is presented.This method can be easily incorporated into a key frame animation system.The angular velocity at an arbitrary time can be calculated easily by our method.This method can also be generalized to smoothly interpolate orientations.展开更多
The branching ratios of ions and the angular distributions of electrons ejected from the Eu 4f^76p_（1/2）nd auto-ionizing states are investigated with the velocity-map-imaging technique.To populate the above auto-ion...The branching ratios of ions and the angular distributions of electrons ejected from the Eu 4f^76p_（1/2）nd auto-ionizing states are investigated with the velocity-map-imaging technique.To populate the above auto-ionizing states,the relevant bound Rydberg states have to be detected first.Two new bound Rydberg states are identified in the region between41150 cm^（-1）and 44580 cm^（-1）,from which auto-ionization spectra of the Eu 4f^76p_（1/2）nd states are observed with isolated core excitation method.With all preparations above,the branching ratios from the above auto-ionizing states to different final ionic states and the angular distributions of electrons ejected from these processes are measured systematically.Energy dependence of branching ratios and anisotropy parameters within the auto-ionization spectra are carefully analyzed,followed by a qualitative interpretation.展开更多
文摘By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integral. The effect of noncanonical strength, off-axis distance and vortex sign on spatial correlation singularities in far field is stressed. Furthermore, far-field OAM spectra and densities are also investigated, and the OAM detection and crosstalk probabilities are discussed. The results show that the number of dislocations of SCS always equals the sum of absolute values of topological charges for canonical or noncanonical vortex pairs. Although the sum of the product of each OAM mode and its power weight equals the algebraic sum of topological charges for canonical vortex pairs, the relationship no longer holds in the noncanonical case except for opposite-charge vortex pairs. The changes of off-axis distance, noncanonical strength or coherence length can lead to a more dominant power in adjacent mode than that in center detection mode, which also indicates that crosstalk probabilities of adjacent modes exceed the center detection probability. This work may provide potential applications in OAM-based optical communication, imaging, sensing and computing.
基金supported by the Program for Liaoning Excellent Talents in University of China(LJQ2014013)the Liaoning Natural Science Foundation of China(2015020066)
文摘This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle avoidance is obtained. The angular velocity is constrained by the controller, so the planned path guarantees the safety of users. According to Lyapunov theory, the controller is designed to maintain stability in terms of solutions of linear matrix inequalities and the controller's performance with safe angular velocity constraints is derived.The simulation and experiment results confirm the effectiveness of the proposed method and verify that the angular velocity of the cushion robot provided safe motion with obstacle avoidance.
基金supported by the National Natural Science Foundation of China (Grant No. 60778048)
文摘Under the quadratic approximation of the Rytov＇s phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.
基金Foundation item： National Natural Science Foundation of China （50805144）
文摘The performance of any inertially stabilized platform （ISP） is strongly related to the bandwidth and accuracy of the angular velocity signals. This paper discusses the development of an optimal state estimator for sensing inertial velocity using low-cost micro-electro-mechanical systems （MEMS） sensors. A low-bandwidth gyroscope is used alone with two low-performance accelerometers to obtain the estimation. The gyroscope has its own limited dynamics and mainly contributes to the low-frequency components of the estimation. The accelerometers have inherent biases and mainly contribute to the high-frequency components of the estimation. Extensive experimental results show that the state estimator can achieve high-performance signals over a wide range of velocities without drifts in both the t- and s-domains. Furthermore, with applications in miniature inertially stabilized platforms, the control characteristic presents a significantly improvement over the existing methods. The method can be also applied to robotics, attitude estimation, and friction compensation.
基金Supported by the Innovation Fund of Shanghai Aerospace Science and Technology(SAST 201308)
文摘The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft.The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adaptive feedback control.An angular velocity feedback tracking algorithm is firstly developed based on the precisely known attitude dynamics of the spacecraft,and the global tracking of the control algorithm is proved based on the Lyapunov analysis.An adaptation mechanism is then designed to deal with the dynamic uncertainties of the spacecraft.Such an adaptation mechanism enables the controller to track any desired angular velocity trajectories even in the presence of uncertain inertia parameters,although it does not guarantee the inertia tensor being precisely identified.To verify the effectiveness of the proposed adaptive control policy,computer simulations on dynamic equations of a spacecraft are conducted and their results are discussed.
文摘Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.
文摘The continuous extrusion forming process for producing large section copper concave bus bar under different extrusion wheel angular velocities was studied by three-dimensional finite element technology based on software DEFORM-3D. The rigid-viscoplastic constitutive equation was employed in the model. The numerical simulation results show that the deformation body flow velocity in the die orifice increases gradually with the increase of the extrusion wheel angular velocity. But slippage between the rod and extrusion wheel occurs when the extrusion wheel angular velocity is high. The effective stress near the die orifice enhances gradually with increasing extrusion wheel angular velocity. High stress is concentrated in adjacent regions of the flash gap. The effective strain gradient is greater near the abutment than that near the die orifice. The effective strain of the product increases gradually with increasing extrusion wheel angular velocity. In the deformation process, the deformation body temperature increases remarkably due to friction and deformation. So the cooling is necessary in the region of the die and tools.
基金supported by the Key Basic Research and Development Program of China(G19980407000)the National Natural Science Foundation of China(40072062)+1 种基金the Foundation of the Open Laboratory of Tectonophysics,China Seismological Bureauthe Post-Doctoral Grant of Ministry of Education,China.
文摘In order to constrain the crustal wave velocity structure in the southernTibetan crust and provide insight into the contribution of crustal composition, geothermal gradientand partial melting to the velocity structure, which is characterized by low average crustalvelocities and widespread presence of low-velocity zone(s), the authors model the crustal velocityand density as functions of depth corresponding to various heat flow values in light of velocitymeasurements at high temperature and high pressure. The modeled velocity and density are regarded ascomparison standards. The comparison of the standards with seismic observations in southern Tibetimplies that the predominantly felsic composition at high heat flow cannot explain the observedvelocity structure there. Hence, the authors are in favor of attributing low average crustalvelocities and low-velocity zone(s) observed in southern Tibet mainly to partial melting. Modelingbased on the experimental results suggests that a melting percentage of 7-12 could account for thelow-velocity zone(s).
基金This work has been partially supported by the Ministry of Science and Technology,Taiwan[Grant Numbers MOST 109-2221-E-019-010 and MOST 110-2221-E-019-042].
文摘In this paper,the estimator-based Global Positioning System(GPS)attitude and angular velocity determination is presented.Outputs of the attitude estimator include the attitude angles and attitude rates or body angular velocities,depending on the design of estimator.Traditionally as a position,velocity and time sensor,the GPS also offers a free attitude-determination interferometer.GPS research and applications to the field of attitude determination using carrier phase or Doppler measurement has been extensively conducted.The rawattitude solution using the interferometry technique based on the least-squares approach is inherently noisy.The estimator such as the Kalman filter(KF)or extended Kalman filter(EKF)can be incorporated into the GPS interferometer,potentially providing several advantages,such as accuracy improvement,reliability enhancement,and real-time characteristics.Three estimator-based approaches are investigated for performance comparison,including(1)KF with measurement involving attitude angles only;(2)EKF with measurements based on attitude angles only;(3)EKF with measurements involving both attitude angles and body angular rates.The assistance from body mounted gyroscopes,if available,can be utilized as the measurements for further performance improvement,especially useful for the case of signal-challenged environment,such as the GPS outages.Modeling of the dynamic process involving the body angular rates and derivation of the related algorithm will be presented.Simulation results for various estimator-based approaches are conducted;performance comparison is presented for the case of GPS outages.
基金Item Sponsored by Fundamental Research Funds for Central Universities of China(HEUCF20151002)
文摘The influences of die parameters on shear strain were investigated by using two-dimensional finite element simulation.New formulas of shear strain were proposed.According to the results of formulas,the shear strain showed a linear dependence on the difference between internal and external fillet radius and the slope was determined by the intersection angle.The simulation results indicated that the velocities of the points from different zones were different in the specimen and the motion trajectories of different points did not follow geometrical laws.The influences of the average velocity and the motion trajectory on shear strain were incorporated in the formula to calculate the shear strain produced during equalchannel angular pressing process.The reliability of simulation results has been partially validated by experiments.
基金The author would like to thank the Nature Science Foundation of China (Grant No.60627001)the Beijing Key Laboratory for Sensor(No.KM200810772001)
文摘In order to find out the influence of the instability of angular velocity of the rotating carrier itself on the stability of silicon micromachined gyroscope, the digital models for relative error of the high and low damping gyroscope's output signal are given respectively, based on the motion equations of the silicon micromachined gyroscope. Theory proves that the output signal error of the silicon micromachined sensor is mainly caused by the instability of damping factor and the angular velocity of the rotating carrier itself. The experiment result indicates that the error of proportionality coefficient of output voltage which is caused by the instability of the angular velocity of the rotating carrier itself reaches to 4.1 %. Theoretical demonstration and experimental verification show that the instability of angular velocity of the rotating carrier itself has an important effect on the stability of low damping silicon micromachined gyroscope.
文摘The study object is the angular output velocity of the drive shaft which is made up of two series-wound cross universal joints. We have deduced the function relation between the angular output velocity and initiative input angle of the drive shaft with double cross universal joints that is based on the calculation formula of the angular output velocity of a single cross universal joint, and by analyzing the relation between the two input angles. By using this function relation, the constant velocity condition of the drive shaft with double cross universal joints＂ is verified. The step-by-step searching algorithm is adopted to obtain the optimal phase angle that leads to the minimum fluctuate index of the angular output velocity in the vary velocity condition. At the same time, we worked out the maximal and minimum value of the angular output velocity, and their initiative input angle. The correctness of the function of the angular output velocity and the step-by-step search algorithm are verified by an ADAMS simulation example.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFE0103300)the open research fund of Songshan Lake Materials Laboratory(Grant No.2023SLABFN26)the Natural Science Foundation of Hubei Province(Grant No.2022CFA088)。
文摘We predict high-velocity magnetic domain wall(DW)motion driven by out-of-plane acoustic spin in surface acoustic waves(SAWs).We demonstrate that the SAW propagating at a 30-degree angle relative to the x-axis of a 128∘Y-LiNbO_(3) substrate exhibits uniform out-of-plane spin angular momentum.This acoustic spin triggers the DW motion at a velocity exceeding 50 m/s in a way that is similar to the spin-transfer-torque effect.This phenomenon highlights the potential of acoustic spin in enabling rapid DW displacement,offering an innovative approach to developing energy-efficient spintronic devices.
文摘In simulation,sometimes we wish to stipulate a specified angular velocity applied to a given frame.Although position,linear velocity and orientation interpolations are well studied,less attention is paid on angular velocity interpolation.In this paper,a new method to smoothly interpolate angular velocity using quaternions is presented.This method can be easily incorporated into a key frame animation system.The angular velocity at an arbitrary time can be calculated easily by our method.This method can also be generalized to smoothly interpolate orientations.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174218)
文摘The branching ratios of ions and the angular distributions of electrons ejected from the Eu 4f^76p_（1/2）nd auto-ionizing states are investigated with the velocity-map-imaging technique.To populate the above auto-ionizing states,the relevant bound Rydberg states have to be detected first.Two new bound Rydberg states are identified in the region between41150 cm^（-1）and 44580 cm^（-1）,from which auto-ionization spectra of the Eu 4f^76p_（1/2）nd states are observed with isolated core excitation method.With all preparations above,the branching ratios from the above auto-ionizing states to different final ionic states and the angular distributions of electrons ejected from these processes are measured systematically.Energy dependence of branching ratios and anisotropy parameters within the auto-ionization spectra are carefully analyzed,followed by a qualitative interpretation.
