Arm position constraints when throwing in three dimensions

1994 ◽  
Vol 72 (3) ◽  
pp. 1171-1180 ◽  
Author(s):  
J. Hore ◽  
S. Watts ◽  
D. Tweed
Keyword(s):  
Degrees Of Freedom ◽  
Angular Position ◽  
Three Dimensional ◽  
Middle Finger ◽  
Three Dimensions ◽  
Position Vector ◽  
Two Dimensional ◽  
Upper Arm ◽  
Work Space ◽  
Ball Release

1. Overarm throwing is a skilled multijoint movement with potentially many degrees of freedom. Considering only the arm > or = 7 degrees of freedom are involved (shoulder 3, elbow 2, wrist 2). For each arm segment 3 degrees of freedom are potentially required to specify its angular position (orientation) at any moment during a throw. Simplification of the control problem for the CNS would occur if there were constraints on these degrees of freedom. The objective was to determine whether such constraints exist at ball release when throwing at targets in different directions using only the arm. 2. The angular positions in three dimensions of the distal phalanx of the middle finger, the hand, the forearm, and the upper arm were simultaneously recorded with search coils as subjects sat with a fixed trunk and threw balls at nine targets in an approximate +/- 40 degree work space. Ball release was signaled by microswitches on the proximal and distal phalanges of the middle finger (proximal and distal triggers). 3. On throwing at any one target the hand at ball release adopted a similar orientation for each throw, i.e., for a particular vertical and horizontal angular position the hand adopted a similar torsional position. On throwing at targets throughout the work space, angular position (rotation) vectors describing hand positions in space at ball release were confined to a two-dimensional surface rather than a three-dimensional volume. This constraint in hand torsion occurred near and at ball release but not throughout the entire throw. It was not due to mechanical factors because such a surface was not obtained when subjects deliberately twisted their arms when throwing. Thus at ball release during a "natural" throw the hand was constrained to 2 of its possible 3 angular degrees of freedom. 4. The same constraint was also found for finger, forearm, and upper arm angular positions in space at ball release as determined at both the proximal and distal triggers. A consequence is that at ball release the entire arm was constrained to 2 of its possible 7 degrees of freedom. 5. The two-dimensional position vector surface for each arm segment was similar to that obtained when pointing with a straight arm at the same targets. In both cases they showed torsion and were twisted like the surface obtained by rotations around the horizontal and vertical axes of a Fick gimbal. However, in some subjects the throwing surfaces were tilted from the vertical.(ABSTRACT TRUNCATED AT 400 WORDS)

Monkey superior colliculus represents rapid eye movements in a two-dimensional motor map

1993 ◽  
Vol 69 (3) ◽  
pp. 965-979 ◽  
Author(s):  
K. Hepp ◽  
A. J. Van Opstal ◽  
D. Straumann ◽  
B. J. Hess ◽  
V. Henn
Keyword(s):  
Eye Movements ◽  
Superior Colliculus ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Eye Position ◽  
Two Dimensional ◽  
Vestibular Nystagmus ◽  
Rapid Eye Movements ◽  
Q Model

1. Although the eye has three rotational degrees of freedom, eye positions, during fixations, saccades, and smooth pursuit, with the head stationary and upright, are constrained to a plane by ListingR's law. We investigated whether Listing's law for rapid eye movements is implemented at the level of the deeper layers of the superior colliculus (SC). 2. In three alert rhesus monkeys we tested whether the saccadic motor map of the SC is two dimensional, representing oculocentric target vectors (the vector or V-model), or three dimensional, representing the coordinates of the rotation of the eye from initial to final position (the quaternion or Q-model). 3. Monkeys made spontaneous saccadic eye movements both in the light and in the dark. They were also rotated about various axes to evoke quick phases of vestibular nystagmus, which have three degrees of freedom. Eye positions were measured in three dimensions with the magnetic search coil technique. 4. While the monkey made spontaneous eye movements, we electrically stimulated the deeper layers of the SC and elicited saccades from a wide range of initial positions. According to the Q-model, the torsional component of eye position after stimulation should be uniquely related to saccade onset position. However, stimulation at 110 sites induced no eye torsion, in line with the prediction of the V-model. 5. Activity of saccade-related burst neurons in the deeper layers of the SC was analyzed during rapid eye movements in three dimensions. No systematic eye-position dependence of the movement fields, as predicted by the Q-model, could be detected for these cells. Instead, the data fitted closely the predictions made by the V-model. 6. In two monkeys, both SC were reversibly inactivated by symmetrical bilateral injections of muscimol. The frequency of spontaneous saccades in the light decreased dramatically. Although the remaining spontaneous saccades were slow, Listing's law was still obeyed, both during fixations and saccadic gaze shifts. In the dark, vestibularly elicited fast phases of nystagmus could still be generated in three dimensions. Although the fastest quick phases of horizontal and vertical nystagmus were slower by about a factor of 1.5, those of torsional quick phases were unaffected. 7. On the basis of the electrical stimulation data and the properties revealed by the movement field analysis, we conclude that the collicular motor map is two dimensional. The reversible inactivation results suggest that the SC is not the site where three-dimensional fast phases of vestibular nystagmus are generated.(ABSTRACT TRUNCATED AT 400 WORDS)

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

Three-Dimensional Nonlinear Dynamics of Nonintegral Riser Bundle

1991 ◽  
Vol 35 (01) ◽  
pp. 40-57
Author(s):  
Nickolas Vlahopoulos ◽  
Michael M. Bernitsas
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Small Strain ◽  
Computer Code ◽  
Three Dimensions ◽  
Central Processor ◽  
Beam Columns ◽  
Central Processor Unit ◽  
Processor Unit ◽  
Strain Model

The dynamic behavior of a nonintegral riser bundle is studied parametrically. The dynamics of each component-riser is analyzed by a three-dimensional, nonlinear, large deflection, small strain model with coupled bending and torsion. Component-risers are slender, thin-walled, extensible or inextensible tubular beam-columns, subject to response and deformation dependent hydrodynamic loads. The con-nector equations of equilibrium are used to derive the connector forces and moments. Substructuring can thus be achieved even though in three dimensions connectors do not impose linearly dependent deflections at substructure interfaces. The developed time incremental and iterative finite-element computer code is used to analyze the effects of water depth, distribution of connectors, distance between component risers and number of finite elements in the numerical model. The problem of total CPU (central processor unit) time and the advantages of substructuring are discussed by running cases of up to 1094 degrees of freedom.

Bringing Dynamic Geometry to Three Dimensions

2015 ◽  
pp. 68-99
Author(s):  
Nicholas H. Wasserman
Keyword(s):  
Teaching And Learning ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Dynamic Geometry ◽  
State Standards ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Common ◽  
K 12

Contemporary technologies have impacted the teaching and learning of mathematics in significant ways, particularly through the incorporation of dynamic software and applets. Interactive geometry software such as Geometers Sketchpad (GSP) and GeoGebra has transformed students' ability to interact with the geometry of plane figures, helping visualize and verify conjectures. Similar to what GSP and GeoGebra have done for two-dimensional geometry in mathematics education, SketchUp™ has the potential to do for aspects of three-dimensional geometry. This chapter provides example cases, aligned with the Common Core State Standards in mathematics, for how the dynamic and unique features of SketchUp™ can be integrated into the K-12 mathematics classroom to support and aid students' spatial reasoning and knowledge of three-dimensional figures.

scholarly journals The magnetorotational instability prefers three dimensions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190622
Author(s):  
Jeffrey S. Oishi ◽  
Geoffrey M. Vasil ◽  
Morgan Baxter ◽  
Andrew Swan ◽  
Keaton J. Burns ◽  
...  
Keyword(s):  
Shear Rate ◽  
Angular Velocity ◽  
Laboratory Experiments ◽  
Three Dimensional ◽  
Linear Instability ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Magnetorotational Instability ◽  
Dynamo Action ◽  
Wide Range

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, S , is near the two-dimensional onset value, S c . For a Keplerian shear, three-dimensional modes are unstable above S  ≈ 0.10 S c , and dominate the two-dimensional modes until S  ≈ 2.05 S c . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05 S c . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

An Intrinsically Three-Dimensional Fractal

2014 ◽  
Vol 24 (06) ◽  
pp. 1430017 ◽  
Author(s):  
M. Fernández-Guasti
Keyword(s):  
Bifurcation Diagram ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Three Dimensional ◽  
Periodic Points ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Hyperbolic Numbers ◽  
Self Similar ◽  
One To One

The quadratic iteration is mapped using a nondistributive real scator algebra in three dimensions. The bound set S has a rich fractal-like boundary. Periodic points on the scalar axis are necessarily surrounded by off axis divergent magnitude points. There is a one-to-one correspondence of this set with the bifurcation diagram of the logistic map. The three-dimensional S set exhibits self-similar 3D copies of the elementary fractal along the negative scalar axis. These 3D copies correspond to the windows amid the chaotic behavior of the logistic map. Nonetheless, the two-dimensional projection becomes identical to the nonfractal quadratic iteration produced with hyperbolic numbers. Two- and three-dimensional renderings are presented to explore some of the features of this set.

scholarly journals Carter's constant and superintegrability

2018 ◽  
Vol 27 (07) ◽  
pp. 1850066
Author(s):  
Payel Mukhopadhyay ◽  
K. Rajesh Nayak
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Simple Observation ◽  
Superintegrable Systems ◽  
Axisymmetric Spacetime ◽  
Three Degrees Of Freedom

Carter's constant is a nontrivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system effectively has two degrees of freedom. We propose an extension to the first version of Carter's theorem to a system having three degrees of freedom to find two functionally independent Carter-like integrals of motion. We further generalize the theorem to a dynamical system with [Formula: see text] degrees of freedom. We further study the implications of Carter's constant to superintegrability and present a different approach to probe a superintegrable system. Our formalism gives another viewpoint to a superintegrable system using the simple observation of separable Hamiltonian according to Carter's criteria. We then give some examples by constructing some two-dimensional superintegrable systems based on this idea and also show that all three-dimensional simple classical superintegrable potentials are also Carter separable.

Prediction of Blade Flutter in a Tuned Rotor

1985 ◽  
Author(s):  
Jianmin Xu ◽  
Zhaohong Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rotating Blades ◽  
Multiple Degrees Of Freedom ◽  
Strip Theory ◽  
Blade Flutter ◽  
Good Agreement

This paper is about blade flutter in a tuned rotor. With the aid of the combination of three dimensional structural finite element method, two dimensional aerodynamical finite difference method and strip theory, the quasi-steady models in which two degrees of freedom for a single wing were considered have been extended to multiple degrees of freedom for the whole blade in a tuned rotor. The eigenvalues solved from the blade motion equation have been used to judge whether the system is stable or not. The calculating procedure has been formed and using it the first stage rotating blades of a compressor where flutter had occurred, have been predicted. The numerical flutter boundaries have good agreement with the experimental ones.

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