The Evaluation of Moments of Bounded Regions Using Spline Approximations of the Boundary

1988 ◽  
Author(s):  
J. Angeles ◽  
Z. Chaoming ◽  
R. Duarte ◽  
H. Ning
Keyword(s):  
Spline Approximation ◽  
Inertia Tensor ◽  
Divergence Theorem ◽  
Axially Symmetric ◽  
Euclidean Spaces ◽  
3 Dimensional ◽  
Gauss Divergence Theorem ◽  
The Subject ◽  
First Moment

Abstract The subject of this paper is the computation of the first three moments of bounded regions imbedded in 2- and 3-dimensional Euclidean spaces. The method adopted here is based upon formulae derived elsewhere, that permit the computation of the said moments — volume, vector first moment and inertia tensor — via integration along the boundary. This is accomplished by the application of Gauss Divergence Theorem to planar and axially-symmetric 3-D regions. It is shown that a spline approximation of the boundary leads to explicit, readily implementable formulae. Two examples are included to illustrate the applicability of the procedure.

The Evaluation of Moments of Regions With Piecewise-Linearly Approximated Boundaries via Line Integration

1989 ◽  
Author(s):  
J. Angeles ◽  
M. J. Al-Daccak
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Inertia Tensor ◽  
Divergence Theorem ◽  
Dimensional Euclidean Space ◽  
Repeated Application ◽  
The Subject ◽  
First Moment

Abstract The subject of this paper is the computation of the first three moments of bounded regions imbedded in the three-dimensional Euclidean space. The method adopted here is based upon a repeated application of Gauss’s Divergence Theorem to reduce the computation of the said moments — volume, vector first moment and inertia tensor — to line integration. Explicit, readily implementable formulae are developed to evaluate the said moments for arbitrary solids, given their piecewise-linearly approximated boundary. An example is included that illustrates the applicability of the formulae.

scholarly journals Newtonian Fractional-dimension Gravity and Rotationally Supported Galaxies

2021 ◽  
Author(s):  
Gabriele U Varieschi
Keyword(s):  
Fractional Dimension ◽  
Newtonian Gravity ◽  
Axially Symmetric ◽  
Local Dimension ◽  
Radial Acceleration ◽  
Modified Newtonian Dynamics ◽  
Newtonian Dynamics ◽  
The Subject ◽  
Symmetric Structures ◽  
Natural Scale

Abstract We continue our analysis of Newtonian Fractional-Dimension Gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces including those with fractional (i.e., non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (Bulge-Dominated Spiral), NGC 6503 (Disk-Dominated Spiral), and NGC 3741 (Gas-Dominated Dwarf). As was done in the general cases of spherically-symmetric and axially-symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dynamics, a leading alternative gravity model which explains the observed properties of these galaxies without requiring the Dark Matter hypothesis. In our model, the MOND acceleration constant a0 ≃ 1.2 × 10−10m s−2 can be related to a natural scale length l0, namely $a_{0} \approx GM/l_{0}^{2}$ for a galaxy of mass M. Also, the empirical Radial Acceleration Relation, connecting the observed radial acceleration gobs with the baryonic one gbar, can be explained in terms of a variable local dimension D. As an example of this methodology, we provide detailed rotation curve fits for the three galaxies mentioned above.

Random sequential packing in Euclidean spaces of dimensions three and four and a conjecture of Palásti

1982 ◽  
Vol 19 (02) ◽  
pp. 382-390 ◽  
Author(s):  
B. Edwin Blaisdell ◽  
Herbert Solomon
Keyword(s):  
Packing Density ◽  
Two Dimensions ◽  
One Dimension ◽  
Euclidean Spaces ◽  
Four Dimensions ◽  
Actual Density ◽  
The Subject

A conjecture of Palásti [11] that the limiting packing density β d in a space of dimension d equals β d where ß is the limiting packing density in one dimension continues to be studied, but with inconsistent results. Some recent correspondence in this journal [7], [8], [13], [14], [15], [16], [18], [19], [20] as well as some other papers indicate a lively interest in the subject. In a prior study [3], we demonstrated that the conjectured value in two dimensions was smaller than the actual density. Here we demonstrate that this is also so in three and four dimensions and that the discrepancy increases with dimension.

scholarly journals Volumes of Polyhedra in Non-Euclidean Spaces of Constant Curvature

2020 ◽  
Vol 66 (4) ◽  
pp. 558-679
Author(s):  
V. A. Krasnov
Keyword(s):  
Hyperbolic Space ◽  
Constant Curvature ◽  
Arbitrary Dimension ◽  
Difficult Problem ◽  
Combinatorial Structure ◽  
Euclidean Spaces ◽  
Spaces Of Constant Curvature ◽  
Simple Polyhedron ◽  
3 Dimensional ◽  
Combinatorial Sense

Computation of the volumes of polyhedra is a classical geometry problem known since ancient mathematics and preserving its importance until present time. Deriving volume formulas for 3-dimensional non-Euclidean polyhedra of a given combinatorial type is a very difficult problem. Nowadays, it is fully solved for a tetrahedron, the most simple polyhedron in the combinatorial sense. However, it is well known that for a polyhedron of a special type its volume formula becomes much simpler. This fact was noted by Lobachevsky who found the volume of the so-called ideal tetrahedron in hyperbolic space (all vertices of this tetrahedron are on the absolute).In this survey, we present main results on volumes of arbitrary non-Euclidean tetrahedra and polyhedra of special types (both tetrahedra and polyhedra of more complex combinatorial structure) in 3-dimensional spherical and hyperbolic spaces of constant curvature K = 1 and K = -1, respectively. Moreover, we consider the new method by Sabitov for computation of volumes in hyperbolic space (described by the Poincare model in upper half-space). This method allows one to derive explicit volume formulas for polyhedra of arbitrary dimension in terms of coordinates of vertices. Considering main volume formulas for non-Euclidean polyhedra, we will give proofs (or sketches of proofs) for them. This will help the reader to get an idea of basic methods for computation of volumes of bodies in non-Euclidean spaces of constant curvature.

scholarly journals Blow-up for the 3-dimensional axially symmetric harmonic map flow into \begin{document}$ S^2 $\end{document}

2019 ◽  
Vol 39 (12) ◽  
pp. 6913-6943
Author(s):  
Juan Dávila ◽  
◽  
Manuel Del Pino ◽  
Catalina Pesce ◽  
Juncheng Wei ◽  
...  
Keyword(s):  
Blow Up ◽  
Harmonic Map ◽  
Axially Symmetric ◽  
3 Dimensional ◽  
Harmonic Map Flow

scholarly journals Relationship between anxiety and static and dynamic balance disorder in subjects with cerebrovascular accident (stroke) diagnosis

2020 ◽  
Vol 18 ◽  
pp. 1-5
Author(s):  
Ana Paula Lemos Ferreira ◽  
Danillo Barbosa
Keyword(s):  
Dynamic Balance ◽  
Multidisciplinary Treatment ◽  
Depression Scale ◽  
Anxiety And Depression ◽  
Hospital Anxiety ◽  
Timed Up And Go ◽  
Balance Disorder ◽  
Postural Imbalance ◽  
The Subject ◽  
First Moment

Background: Sensory systems are responsible for maintaining balance, being vision, vestibular and somatosensory, and all these systems suffer changes in patients with stroke sequelae and studies bet that anxiety is likely to influence the inability of the subject to use these systems, enhancing the postural imbalance in stroke patients. Objective: To analyze the interference of anxiety on the static and dynamic balance of patients diagnosed with stroke. Methods: Fifteen patients with stroke, aged 40 to 80 years, were assessed using the Hospital Anxiety and Depression Scale, Timed Up and Go test for dynamic balance and the Berg Scale for static balance. Data were tabulated in Excel and analyzed using SPSS - Statistical Package for Social Science (version 20.0). Results: Significant values were found for the correlation between anxiety and balance, in which the results analyzed showed that the balance of patients with stroke can be negatively exacerbated due to the anxiety that affects them. Conclusion: It can be concluded from these results that anxiety can alter the balance of these patients and thus, it is shown the importance of a multidisciplinary treatment from the first moment to leverage the treatment.

THE STATIC AXIALLY SYMMETRIC SELF-DUAL YANG-MILLS FIELDS AND SURFACES OF NEGATIVE CURVATURE

1986 ◽  
Vol 01 (01) ◽  
pp. 193-210
Author(s):  
BO-YU HOU ◽  
BO-YUAN HOU ◽  
PEI WANG
Keyword(s):  
Minkowski Space ◽  
Negative Curvature ◽  
Complete Integrability ◽  
Axially Symmetric ◽  
Yang Mills ◽  
3 Dimensional ◽  
Variable Curvature ◽  
Dimensional Minkowski Space ◽  
Geometric Picture ◽  
Adjoint Space

An explicit geometric picture about the complete integrability of the static axially symmetric self-dual Yang-Mills equation and the gravitational Ernst equation is presented. The corresponding soliton surfaces in adjoint space (3-dimensional Minkowski space) has negative variable curvature. The Riccati equation is also given, so that the integrability of the Bäcklund transformation gets the confirmation.

Sign in / Sign up

Export Citation Format

Share Document