Velocity Dispersion σ_(aper)Aperture Corrections as a Function of Galaxy Properties from Integral-field Stellar Kinematics of 10,000 MaNGA Galaxies

The second moment of the stellar velocity within the effective radius,denoted by σ^(2)_(e),is a crucial quantity in galaxy studies,as it provides insight into galaxy properties and their mass distributions.However,large spectroscopic surveys typically do not measure σ_(e) directly,instead providing σ_(aper),the second moment of the stellar velocity within a fixed fiber aperture.In this paper,we derive an empirical aperture correction formula,given byσ_(aper)/σ_(e)=(R_(aper)/R_(e))^(α),using spatially resolved stellar kinematics extracted from approximately 10,000 Sloan Digital Sky Survey-Mapping Nearby Galaxies at Apache Point Observatory integral field unit observations.Our analysis reveals a strong dependence ofαon the r-band absolute magnitude M_(r),g-i color,and Sérsic index nSer,whereαvalues are lower for brighter,redder galaxies with higher Sérsic indices.Our results demonstrate that the aperture correction derived from previous literature on early-type galaxies cannot be applied to predict the aperture corrections for galaxies with intermediate Sérsic indices.We provide a lookup table ofαvalues for different galaxy types,with parameters in the ranges of-18>M_(r)>-24,0.4<g-i<1.6,and 0<n_(Ser)<8.A Python script is provided to obtain the correction factors from the lookup table.

Kinematics and dynamics analysis of a 3-7R parallel decoupling mechanism

One kind of movable-pair analysis method is adopted to analyze the configuration of a 3-7R （revolute-pair） parallel decoupling mechanism, and the mechanism＇s characteristics are summarized. The mechanism has three orthogonal distributional branch-chains, and all movable pairs are rotational joints. The movable platform of the mechanism has x, y, z translational decoupling directions. Furthermore, in order to verify the mechanism＇s decoupling characteristics, the mechanism＇s kinematics analysis is solved, and the mechanism＇s direct/inverse kinematics model, input/output velocities and accelerations are deduced, which confirm its decoupling movement characteristics. Finally, one kind of mechanism link decomposed-integrated approach is adopted, and the mechanism＇s dynamics model is completed with the Lagrange method, which also proves its decoupling force characteristics. All of these works provide significant theory for the further study of the mechanism＇s control strategy, design, path planning etc.

Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory

The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.

Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory

Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.

Kinematics and Dynamics Analysis of a Quadruped Walking Robot with Parallel Leg Mechanism

It is desired to require a walking robot for the elderly and the disabled to have large capacity,high stiffness,stability,etc.However,the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function.Therefore,Improvement of enhancing capacity and functions of the walking robot is an important research issue.According to walking requirements and combining modularization and reconfigurable ideas,a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed.The proposed robot can be used for both a biped and a quadruped walking robot.The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized.The results show that performance of the walking robot is optimal when the circumradius R,r of the upper and lower platform of leg mechanism are 161.7 mm,57.7 mm,respectively.Based on the optimal results,the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory,and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed,which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process.Besides laying a theoretical foundation for development of the prototype,the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.

Kinematics and dynamics analysis of a three-degree-of-freedom parallel manipulator

Kinematics and dynamics analyses were performed for a spatial 3-revolute joint-revolute joint-clylindric pair(3-RRC) parallel manipulator.This 3-RRC parallel manipulator is composed of a moving platform,a base platform,and three revolute joint-revolute joint-column pair chains which connect the moving platform and the base platform.Firstly,kinematics analysis for 3-RRC parallel manipulator was conducted.Next,on the basis of Lagrange formula,a simply-structured dynamic model of 3-RRC parallel manipulator was derived.Finally,through a calculation example,the variation of motorial parameters of this 3-RRC parallel manipulator,equivalent moment of inertia,driving force/torque and energy consumption was discussed.The research findings have important significance for research and engineering projects such as analyzing dynamic features,mechanism optimization design and control of 3-RRC parallel manipulator.

Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve （or vice versa）. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the ＂galactic rotation number＂ that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity （such as the ＂flat＂ value in a typical ro- tation curve） and Rg the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.

Cross-method Analysis of Corotation Radii Data Set for Spiral Galaxies

A corotation radius is a key characteristic of disk galaxies that is essential to determine the angular speed of the spiral structureΩ_p,and therefore understand its nature.In the literature,there are plenty of methods to estimate this value,but do these measurements have any consistency?In this work,we collected a data set of corotation radius measurements for 547 galaxies,300 of which had at least two values.An initial analysis reveals that most objects have rather inconsistent corotation radius positions.Moreover,a significant fraction of galactic disks is distinguished by a large error coverage and almost uniform distribution of measurements.These findings do not have any relation to spiral type,Hubble classification,or presence of a bar.Among other reasons,obtained results could be explained by the transient nature of spirals in a considerable part of galaxies.We have made our collected data sample publicly available,and have demonstrated on one example how it could be useful for future research by investigating a winding time value for a sample of galaxies with possible multiple spiral arm patterns.

A Fermi-LAT Study of Globular Cluster Dynamical Evolution in the Milky Way:Millisecond Pulsars as the Probe

Using archival Fermi-LAT data with a time span of~12 yr,we study the population of Millisecond Pulsars(MSPs)in Globular Clusters(GlCs)and investigate their dependence on cluster dynamical evolution in the Milky Way.We show that theγ-ray luminosity(L_(γ))and emissivity(i.e.,ε_(γ)=L_(γ)/M,with M the cluster mass)are good indicators of the population and abundance of MSPs in GlCs,and they are highly dependent on the dynamical evolution history of the host clusters.Specifically speaking,the dynamically older GlCs with more compact structures are more likely to have larger L_(γ)andε_(γ),and these trends can be summarized as strong correlations with cluster stellar encounter rateΓand the specific encounter rate(Λ=Γ/M),with L_(γ)∝Γ^(0.7±0.11)andε_(γ)∝Λ^(0.73±0.13)for dynamically normal GlCs.However,as GlCs evolve into deep core collapse,these trends are found to be reversed,implying that strong encounters may have lead to the disruption of Low-Mass X-ray Binaries and ejection of MSPs from core-collapsed systems.Besides,the GlCs are found to exhibit largerε_(γ)with increasing stellar mass function slope(ε_(γ)∝10^((0.52±0.1)α)),decreasing tidal radius(ε_(γ)∝R_(t)^(-10±0.22))and distances from the Galactic Center(GC,ε_(γ)∝R_(gc)^(-1.13±0.21)).These correlations indicate that,as GlCs losing kinetic energy and spiral in toward the GC,tidal stripping and mass segregation have a preference in leading to the loss of normal stars from GlCs,while MSPs are more likely to concentrate to cluster center and be deposited into the GC.Moreover,we gaugeε_(γ)of GlCs is~10-1000 times larger than the Galactic bulge,the latter is thought to reside thousands of unresolved MSPs and may be responsible for the GC 7-ray excess,which supports that GlCs are generous contributors to the population of MSPs in the GC.

New HⅠObservations Toward the NGC 5055 Galaxy Group with FAST

We report a new high-sensitivity HⅠmapping observation of the NGC 5055 galaxy group over an area of 1°.5×0°.75 with the Five-hundred-meter Aperture Spherical radio Telescope(FAST).Our observation reveals that the warped HⅠdisk of NGC 5055 is more extended than what was previously observed by WSRT,out to239(61.7 kpc).The total HⅠmass of NGC 5055 is determined to be~1.1×10^(10)M_Θ.We identified three HⅠclouds with HⅠmasses of the order of~10^(7)M_Θat the southeastern edge of the HⅠdisk,as well as a candidate high-velocity cloud with an HⅠmass of(1.2±0.5)×10^(6)M_Θto the north of NGC 5055.The HⅠcontent of UGCA337 is robustly detected for the first time by the FAST observations.It has a narrow HⅠlinewidth of W_(50)=17.4±3.8 km s^(-1)with a total HⅠmass of(3.5±0.3)×10^(6)M_Θ.Comparing the gas content and g-r color of UGCA 337 with typical low-mass dwarf galaxies,UGCA 337 appears relatively gas-poor despite its blue color.This suggests that UGCA 337 may have undergone gas stripping in the past.We also analyzed the possible origin of the diffuse HⅠclouds located at the outskirts of NGC 5055,and speculate that they might be the remnant features of a merger event in the past.

Evaluation of slope stability through rock mass classification and kinematic analysis of some major slopes along NH-1A from Ramban to Banihal, North Western Himalayas

The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index(GSI),rock mass rating(RMR),continuous slope mass rating(CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating(SSR)for the factor of safety(FoS)of 1.2 and 1 respectively.Q-slope with probability of failure(PoF)1%gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR&GSI with correlation coefficient(R 2)value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

The analyses of kinematic wave properties of a new dynamics model for traffic flow are carried out. The model does not exhibit the problem that one characteristic speed is always greater than macroscopic traffic speed, and therefore satisfies the requirement that traffic flow is anisotropic. Linear stability analysis shows that the model is stable under certain condition and the condition is obtained. The analyses also indicate that the model has a hierarchy of first- and second-order waves and allows the existence of both smooth traveling wave and shock wave. However, the model has a distinctive criterion of shock wave compared with other dynamics models, and the distinction makes the model more realistic in dealing with some traffic problems such as wrong-way travel analysis.

Kinematics of the Open Cluster System in the Galaxy

Absolute proper motions and radial velocities of 202 open clusters in the solar neighborhood, which can be used as tracers of the Galactic disk, are used to investigate the kinematics of the Galaxy in the solar vicinity, including the mean heliocentric velocity components （u1, u2, u3） of the open cluster system, the characteristic velocity dispersions （σ1,σ2,σ3）, Oort constants （A, B） and the large-scale radial motion parameters （C, D） of the Galaxy. The results derived from the observational data of proper motions and radial velocities of a subgroup of 117 thin disk young open clusters by means of a maximum likelihood algorithm are： （u1,u2,u3） = （-16.1 ± 1.0,-7.9 ±1.4,-10.4±1.5） km·s^-1, （σ1,σ2,σ3） = （17.0±0.7, 12.2±0.9, 8.0±1.3） km·S^-1, （A, B） = （14.8±1.0, - 13.0±2.7） km·s^-1 kpc^-1, and （C, D） = （1.5 ± 0.7, -1.2 ±1.5） km·s^-1 kpc^-1. A discussion on the results and comparisons with what was obtained by other authors is given.

Merger Dynamics of the Pair of Galaxy Clusters-A399 and A401

Convincing evidence for a past interaction between the two rich clusters A399 and A401 was recently found in the X-ray imaging observations. We examine the structure and dynamics of this pair of galaxy clusters. A mixture-modeling algorithm was applied to obtain a robust partition into two clusters, which allowed us to discuss the virial mass and velocity distribution of each cluster. Assuming that these two clusters follow a linear orbit and they have once experienced a close encounter, we model the binary cluster as a two-body system. As a result, four gravitationally bound solutions are obtained. The recent X-ray observations seem to favor a scenario in which the two clusters with a true separation of 5.4h-1 Mpc are currently expanding at 583 km s-1 along a direction with a projection angle of 67.5°, and they will reach a maximum extent of 5.65 h-1 Mpc in about 1.0 h-1 Gyr.

Stellar kinematics and populations out to 1.5 effective radii in the elliptical galaxy NGC 4636

We present high quality long slit spectra along the major and minor axes out to 1.5 effective radii of the massive galaxy NGC 4636 taken by the Hobby-Eberly Telescope. Using the Fourier Correlation Quotient method, we measured the stellar line-of-sight velocity distribution along the axes. Furthermore, six Lick/IDS indices （Hβ, Mgb, Fe5015, Fe5270, Fe5335, Fe5406） are derived from the clean spectrum. By comparing the measured absorption line strengths with the predictions of Simple Stellar Population （SSP） models, we derived ages, total metallicity and a abundance profiles of the galaxy. This galaxy presents old and [α/Fe] overabundant stellar populations. Indeed, using the SSP model, we obtained the broadband color profiles. The theoretical colors match well with the measured colors and present red sharp peaks at the galaxy center. The sharp peaks of the colors are mainly shaped by the high metallicity in the galaxy＇s center. Interestingly, the galaxy has steep negative metaUicity gradients, but the trend flattens outwards. This result likely suggests that the center and outer regions of the galaxy formed through different formation processes.

Gravito-Electrodynamics in Galaxy Rotation Curves. ENG: An Extended Newtonian Gravitation

An extended Newtonian gravitation (ENG) model was developed to explain the rotation curves in galaxies and galaxy clusters. ENG requires the knowledge of a parameter that is a function of the mass of the gravitational source. An approximate eq. for that parameter was obtained (for disk galaxies) that yields asymptotic speeds close to binned measured data. ENG yielded larger circular speeds for galaxy clusters when compared with the MOND results. A classical gravito-electromagnetic model (which neither is based on Einstein GR, nor on gravito-magnetism only) was developed which yielded asymptotic circular speeds very small compared to experimental results. However when ENG was used to develop an extended gravito-electromagnetic model, it yielded results compatible with MOND results for simulated galaxies and larger than MOND results for a simulated galaxy cluster. This model showed measurable increase in the circular speed when compared to ENG alone in the galaxy cluster. The need for modifying the Einstein field equation to address the dark matter problem in the framework of the ENG model was illustrated.

Dynamics Analysis of Close-coupling Multiple Helicopters System

The particularity and practicality of harmony operations of close-coupling multiple helicopters indicate that the researches on it are urgent and necessary, Using the model that describes two hovering helicopters carrying one heavy load, an inertia coordinate system and body coordinate systems of each sub-system are established. A nonlinear force model is established too. The equilibrium computation results can be regarded as the reference control inputs of the flight control system under hovering or low-speed flight condition. After the establishment of a translation kinematics model and a posture kinematics model, a coupling dynamics model of the multiple helicopter system is set up. The results can also be regarded as the base to analyze stabilization and design a controller for a close-coupling multiple helicopters harmony operation system.

DYNAMICS ANALYSIS OF 2-DOF SPHERICAL PARALLEL MECHANISM

The analytical formulations of the velocity and the acceleration of a 2-DOF spherical parallel mechanism are derived by the screw theory. Based on building its dynamics model by the principle of virtual work and reciprocal product of the screw, the equation of the motor moment is obtained. Through the transformation of dynamics model, the configuration space method of the dynamics equation and the corresponding coefficients are presented. Finally, the result of an example shows that the inertia moment and the gravity play a more important role than the coriolis and centrifugal moment, and the former is ten times of the latter in the magnitude. So, the latter can be neglected only when the velocity of mechanism is very slow.

INVERSE KINEMATIC AND DYNAMIC ANALYSIS OF A 3-DOF PARALLEL MECHANISM

According to the structure character of the passive sub-chain of the 3TPS-TPparallel mechanism, the kinematic constraint equations of the movable platform are established,based on which the closed-form inverse kinematics formula of the parallel mechanism are presented.Through parting the spherical joints of the active sub-chains and using the force and momentequilibrium of both the active sub-chains and passive sub-chain, the constraint forces acting on theparted joints are determined. Subsequently, the analytic expressions of the actuator driving forcesare derived by means of the force equilibrium of the upper links of active sub-chains.

Kinematics Analysis and Optimization of the Fast Shearing-extrusion Joining Mechanism for Solid-state Metal

Dynamical Joining of the solid-state metal is the key technology to realize endless hot rolling. The heating and laser welding method both require long joining time. Based on super deformation method, a 7-bar and 2-slider mechanism was developed in Japan, and the joining time is less than 0.5 s, however the length of each bar are not reported and this mechanism is complex. A relatively simple 6-bar and 1-slider mechanism is put forward, which can realize the shearing and extrusion motion of the top and bottom blades with a speed approximately equal to the speed of the metal plates. In order to study the kinematics property of the double blades, based on complex vector method, the multi-rigid-body model is built, and the displacement and speed functions of the double blades, the joining time and joining thickness are deduced, the kinematics analysis shows that the initial parameters can＇t satisfy the joining process. Hence, optimization of this mechanism is employed using genetic algorithm（GA） and the optimization parameters of this mechanism are obtained, the kinematics analysis show that the joining time is less than 0.1 s, the joining thickness is more than 80% of the thickness of the solid-state metal, and the horizontal speeds of the blades are improved. A new mechanism is provided for the joining of the solid-state metal and a foundation is laid for the design of the device.