A dynamic-kinematic method for computing vertical motion
Dynamic-kinematic method for computing vertical motion velocity from winds
VELOCITY MEASUREMENT↗
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Comparisons of Kinematics and Dynamics Simulation Software Tools
Kinematic and dynamic analyses for moving bodies are essential to system engineers and designers in the process of design and validations. 3D visualization and motion simulation plus finite element analysis (FEA) give engineers a better way to present ideas and results. Marshall Space Flight Center (MSFC) system engineering researchers are currently using IGRIP from DELMIA Inc. as a kinematic simulation tool for discrete bodies motion simulations. Although IGRIP is an excellent tool for kinematic simulation with some dynamic analysis capabilities in robotic control, explorations of other alternatives with more powerful dynamic analysis and FEA capabilities are necessary. Kinematics analysis will only examine the displacement, velocity, and acceleration of the mechanism without considering effects from masses of components. With dynamic analysis and FEA, effects such as the forces or torques at the joint due to mass and inertia of components can be identified. With keen market competition, ALGOR Mechanical Event Simulation (MES), MSC visualNastran 4D, Unigraphics Motion+, and Pro/MECHANICA were chosen for explorations. In this study, comparisons between software tools were presented in terms of following categories: graphical user interface (GUI), import capability, tutorial availability, ease of use, kinematic simulation capability, dynamic simulation capability, FEA capability, graphical output, technical support, and cost. Propulsion Test Article (PTA) with Fastrac engine model exported from IGRIP and an office chair mechanism were used as examples for simulations.
Yeu-Sheng Paul Shiue↗
Shepherding of the Uranian rings. I - Kinematics. II - Dynamics
The possible kinematical relationships between the Uranian rings and all ten newly discovered satellites of Uranus are examined. Observational evidence is presented for interactions between 1986U7 and 1986U8 and the epsilon, delta, and gamma rings. The likelihood that these two satellites are shepherding the epsilon ring and are responsible for some of its internal structure is assessed, and the results are used to propose a reduction in the ring radius scale. It is also proposed that 1986U7 and 1986U8 are the inner and outer shepherds for the epsilon ring, that 1986U7 is the outer shepherd for the delta ring, and that 1986U8 is an outer shepherd for the gamma ring. The results of theoretical investigations of planetary ring dynamics are then applied to these associations, and their dynamical significance is evaluated. The resonant torques which the satellites exert on each ring are calculated and compared to the viscous torque which transports angular momentum outward through the ring and to the atmospheric-drag torque which causes the ring's orbit to decay.
Porco, Carolyn C.↗
Spatial operator approach to under-actuated manipulator kinematics and dynamics
A study is made of the kinematics and dynamics of under-actuated manipulators. The presence of passive hinges causes the kinematics and dynamics of these manipulators to be considerably more complex when compared with fully actuated manipulators. Techniques from the spatial operator algebra are used to develop expressions for the generalized Jacobian, the mass matrix, and an efficient inverse dynamics computational algorithm.
Jain, A.↗
The kinematics and dynamics of space manipulators - The virtual manipulator approach
Future robotic manipulator systems will be required to perform complex tasks in space such as satellite repair. These robotic manipulators will encounter a number of kinematic, dynamic, and control problems caused by the dynamic coupling between the manipulators and its spacecraft. This dynamic coupling also makes it difficult to analyze these systems. This paper introduces a new analytical modeling method for space manipulators called the Virtual Manipulator (VM), which has a fixed based in inertial space at a point called a Virtual Ground. The kinematics and dynamics of the manipulator, spacecraft, and payload can be described relatively easily in terms of the VM. With its fixed base, the Virtual Manipulator is shown to have the potential to be an effective aid for the analysis, design, and development of future space manipulator systems.
Vafa, Z.↗
Graph Theory Roots of Spatial Operators for Kinematics and Dynamics
Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.
Jain, Abhinandan↗
Kinematics and dynamics of a six-degree-of-freedom robot manipulator with closed kinematic chain mechanism
This paper deals with a class of robot manipulators built based on the kinematic chain mechanism (CKCM). This class of CKCM manipulators consists of a fixed and a moving platform coupled together via a number of in-parallel actuators. A closed-form solution is derived for the inverse kinematic problem of a six-degre-of-freedom CKCM manipulator designed to study robotic applications in space. Iterative Newton-Raphson method is employed to solve the forward kinematic problem. Dynamics of the above manipulator is derived using the Lagrangian approach. Computer simulation of the dynamical equations shows that the actuating forces are strongly dependent on the mass and centroid of the robot links.
Nguyen, Charles C.↗
The spatial distribution, kinematics, and dynamics of the galaxies in the region of Abell 2634 and 2666
A total of 663 galaxies with known redshifts in a 12 deg x 12 deg field centered on A2634, including 211 new measurements, are used to study in detail the structure of the region. In it we find six main galaxy concentrations: the nearby clusters A2634 and A2666, two groups in the vicinity of A2634, and two distant clusters at approximately 18,000 (A2622) and approximately 37,000 km/s seen in projection near the core of A2634. For A2634, the most richly sampled of those concentrations, we are able to apply strict cluster membership criteria. Two samples - one containing 200 galaxies within 2 deg from the cluster center and a second, magnitude-limited, of 118 galaxies within the central half degree - are used to examine the structure, kinematics, dynamics, and morphological segregation of the cluster. We show that early type galaxies appear to be a relaxed system, while the spiral population eschews the center of the cluster and exhibits both a multimodal velocity distribution and a much larger velocity dispersion that the ellipticals. We propose that the spiral galaxies of A2634 represent a dynamically young cluster population. For the galaxy component of A2634, we find no evidence of significant substructure in the central regions. We also conclude that the adoption of lenient membership criteria that ignore the dynamical complexity of A2634 are unlikely to be responsible for the conflicting results reported on the motion of this cluster with respect ot the CMB. The kinematical and dynamical analysis is extended to A2634's close companion, A2666, and the two distant background clusters.
Scodeggio, Marco↗
Alternate Forms of Relative Attitude Kinematics and Dynamics Equations
In this paper the alternate forms of the relative attitude kinematics and relative dynamics equations are presented. These developments are different from the earlier developments that have been presented in other publications. The current forms of equations have the advantage of being simpler than earlier ones. These equations are applied in developing the necessary kinematics and dynamics for relative navigation in formation flying and virtual platforms. These equations also have application in the implementation of nonlinear full state feedback and nonlinear output feedback control for large attitude angle acquisition and tracking. This paper presents simulations from such a full state feedback control application.
Xing, Guang Q.↗
A spatial, kinematical, and dynamical analysis of Abell 400
The paper presents a detailed spatial, kinematical, and dynamical analysis for the cluster A400, based on a nearly complete redshift survey of bright galaxies within 1 Mpc of the cluster center. A dispersed component with a high fraction of spiral galaxies at a velocity of 8200 km/s, and a background group with a mean velocity of 13,400 km/s are identified. It is proposed that the main body of A400 is composed of at least two individual subclusters. If subclustering is ignored, the derived dispersion of the 88 galaxies with measured velocities within 4000 km/s of the bright dumbbell galaxy near the cluster center is 702 km/s. When kinematic information is used to split A400 into likely subclusters, the velocity dispersions of the individual units which make up this cluster are on the order of 200-300 km/s. If A400 is considered a single entity, the inferred blue mass-to-light ratio is 1210 solar masses/solar luminosities. It is argued that A400 is an example of a presently occurring merger, and that the individual components of the dumbbell galaxy were once individual D galaxies within the premerger subclusters.
Beers, Timothy C.↗
Constraints on Pacific plate kinematics and dynamics with global positioning system measurements
A measurement program designed to investigate kinematic and dynamic aspects of plate tectonics in the Pacific region by means of satellite observations is proposed. Accuracy studies are summarized showing that for short baselines (less than 100 km), the measuring accuracy of global positioning system (GPS) receivers can be in the centimeter range. For longer baselines, uncertainty in the orbital ephemerides of the GPS satellites could be a major source of error. Simultaneous observations at widely (about 300 km) separated fiducial stations over the Pacific region, should permit an accuracy in the centimeter range for baselines of up to several thousand kilometers. The optimum performance level is based on the assumption of that fiducial baselines are known a priori to the centimeter range. An example fiducial network for a GPS study of the South Pacific region is described.
Dixon, T. H.↗
Kinematics and dynamics of vortex rings in a tube
Kinematic theory and flow visualization experiments were combined to examine the dynamic processes which control the evolution of vortex rings from very low to very high Reynolds numbers, and to assess the effects of the wall as a vortex ring travels up a tube. The kinematic relationships among the size, shape, speed, and strength of vortex rings in a tube were computed from the theory. Relatively simple flow visualization measurements were used to calculate the total circulation of a vortex rings at a given time. Using this method, the strength was computated and plotted as a function of time for experimentally produced vortex rings. Reynolds number relationships are established and quantitative differences among the three Reynolds number groups are discussed.
Brasseur, J. G.↗
On the statistical theory of self-gravitating collisionless dark matter flow: High order kinematic and dynamic relations
Dark matter, if it exists, accounts for five times as much as ordinary baryonic matter. To better understand the self-gravitating collisionless dark matter flow on different scales, a statistical theory involving kinematic and dynamic relations must be developed for different types of flow, e.g., incompressible, constant divergence, and irrotational flow. This is mathematically challenging because of the intrinsic complexity of dark matter flow and the lack of a self-closed description of flow velocity. Here, this paper extends our previous work on second-order statistics Xu to kinematic relations of any order for any type of flow. Dynamic relations were also developed to relate statistical measures of different orders. The results were validated by N-body simulations. On large scales, we found that (i) third-order velocity correlations can be related to density correlation or pairwise velocity; (ii) the pth-order velocity correlations follow ∝ a (p+2)/2 for odd p and ∝ a p/2 for even p, where a is the scale factor; (iii) the overdensity δ is proportional to density correlation on the same scale, $\langle$δ$\rangle$∝$\langle$δδ'$\rangle$; (iv) velocity dispersion on a given scale r is proportional to the overdensity on the same scale. On small scales, (i) a self-closed velocity evolution is developed by decomposing the velocity into motion in haloes and motion of haloes; (ii) the evolution of vorticity and enstrophy are derived from the evolution of velocity; (iii) dynamic relations are derived to relate second- and third-order correlations; (iv) while the first moment of pairwise velocity follows $\langle$Δu L $\rangle$=-Har (H is the Hubble parameter), the third moment follows $\langle$(Δu L ) 3 $\rangle$ ∝ ε u ar that can be directly compared with simulations and observations, where ε u ≈ 10 -7 m 2 /s 3 is the constant rate for energy cascade; (v) the pth order velocity correlations follow ∝ a (3p-5)/4 for odd p and ∝ a 3p/4 for even p. Finally, the combined kinematic and dynamic relations lead to exponential and one-fourth power-law velocity correlations on large and small scales, respectively.
79 ASTRONOMY AND ASTROPHYSICS↗
RR Lyrae stars and the distant Galactic halo - Distribution, chemical composition, kinematics, and dynamics
Published observational data on 29 outer-Galactic-halo RR Lyr stars (Saha, 1984, and Saha and Oke, 1984) and from other surveys are analyzed to characterize the mass distribution, chemical composition, kinematics, and dynamics of the outer Galaxy (up to galactocentric radius R = 40 kpc). The results are presented in graphs and tables and discussed. Findings reported include a rapid fall-off of RR Lyr density at R = 25 kpc, Fe/H varying from -1.0 to -2.2 (with two stars at -0.5), no net Fe/H gradient in the far halo, and Galactic mass (from dynamical computations) about 3 x 10 to the 11th solar mass within R = 25 kpc.
Saha, A.↗
The kinematics and dynamics of the rich cluster of galaxies Abell 539
A sample of 289 redshifts within 10 deg of the center of the cluster A539 have been obtained in order to investigate the cluster kinematics and dynamics. Within 1 Mpc of the center, the physical parameters of A539 are found to be typical of those of rich clusters. It is shown that early-type galaxies are more concentrated toward the cluster center and that the velocity distributions of early-type and late-type galaxies differ marginally.
Ostriker, Eve C.↗
A Study of the Kinematic and Dynamic Processes associated with Mesoscale Snowbands in a Midwest United States Snowstorm on 5 February 2020
Mesoscale snowbands are frequently responsible for dumping large amounts of snow over a relatively small region and pose a considerable forecasting challenge. The present study focuses on the mesoscale snowbands observed on 5 February 2020 over the Midwest United States. In order to improve the forecasting of mesoscale snowbands, it is important to understand the processes that organize these features. To this end, we are investigating the kinematic and dynamic processes that shape the mesoscale snowbands using a combination of high-altitude airborne radar, in-situ aircraft measurements, surface observations, and model simulations. This presentation will primarily focus on the three-dimensional structure of the mesoscale snowbands in terms of EXRAD reflectivity and horizontal winds. The horizontal winds are retrieved from the EXRAD scanning-beam Doppler velocities using a VAD technique. These winds, in combination with virtual potential temperature taken from the HRRR operational analysis, are used to compute the bulk Richardson number in order to investigate any contributions to banding features that might be tied to Kelvin-Helmholtz instability. Our analysis does not support the presence of Kelvin-Helmholtz instability. That said, low, but not subcritical, Richardson numbers were found near the top of some banding features in this event and it is possible that the model analysis is smoothing out the virtual potential temperature fields. Finally, we present arguments for using a flight module designed to sample the along-band structures with particular emphasis on observing generating cells and low-level microphysics.
Charles N. Helms↗
Kinematics and dynamics of disclination lines in three-dimensional nematics
An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameter Q is derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues of Q cross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives of Q on the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation for Q, analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. Finally, the analytic results are shown to be in agreement with three-dimensional numerical calculations based on a singular Maier–Saupe free energy that allows for anisotropic elasticity.
36 MATERIALS SCIENCE↗
Judging rolling wheels: Dynamic and kinematic aspects of rotation-translation coupling
Four experiments were carried out to investigate observers' abilities to judge rolling motions. The experiments were designed to assess whether two important aspects of such motions are appreciated: the kinematic coupling of rotation and translation, and the dynamic effects of gravity. Different motion contexts of rolling wheels were created using computer-generated displays. The first experiment involved wheels rolling down an inclined plane. Observers spontaneously appreciated the anomaly of wheels that failed to accelerate, but they were not able to differentiate between different acceleration functions. Moreover, their judgements were almost exclusively based on the translation component of the rolling motion, neglecting the rotation component. In a second experiment it was found that observers could accurately estimate the perimeter of various objects. Thus, their inability to consider rotation information is not attributable to misperceptions of the geometry of wheels. In a third experiment the finding that rolling wheels appear to overrotate was replicated; however, findings from this experiment also showed, together with those from a fourth experiment, that observers are able to make very accurate judgments about translation-rotation coupling in rolling wheels when information is provided about the orientation of the wheel and the texture of the surface on which it rolls.
Hecht, Heiko↗