scholarly journals On some properties of normally-inflective complexes with simple inflective center in $E_3$

2021 ◽  
pp. 112
Author(s):  
Ye.N. Ishchenko
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Parametric Families ◽  
Straight Lines ◽  
Arbitrary Curve

In the paper, we consider the special degenerate class of mormally-inflective complexes with simple inflective center in three-dimensional Euclidean space $E_3$. We prove that to construct this class of complexes one should take an arbitrary curve and draw sheaf of straight lines through each point of this curve. For arbitrary normally-inflective complex with simple inflective center we establish that such complex is fibered into two one-parametric families of congruences.

A Plethora of Non-Bending Surfaces of Revolution: Classifications and Explicit Parameterizations

2021 ◽  
pp. 219-241
Author(s):  
Vladimir Pulov ◽  
Ivailo M. Mladenov
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Surfaces Of Revolution ◽  
Parametric Families ◽  
Rotational Surfaces ◽  
Topological Transformations

As the title itself suggests here we are presenting extremely reach two/three parametric families of non-bending rotational surfaces in the three dimensional Euclidean space and provide the necessary details about their natural classifications and explicit parameterizations. Following the changes of the relevant parameters it is possible to trace out the ``evolution'' of these surfaces and even visualize them through their topological transformations. Many, and more deeper questions about their metrical properties, mechanical applications, etc. are left for future explorations.

scholarly journals О восстановлении тензорного поля второго ранга с нулевым следом по неполным данным

2020 ◽  
pp. 38-47
Author(s):  
Zyaudin Medzhidov
Keyword(s):  
Euclidean Space ◽  
Displacement Field ◽  
Tensor Field ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Rank 2 ◽  
Straight Lines ◽  
Integral Data ◽  
Linear Integrals

An algorithm for the complete reconstruction of a tensor field of rank 2 in three-dimensional Euclidean space on incomplete integral data is constructed. The solenoid part of the field is constructed using linear integrals on straight lines that intersect a curve at infinity, and the displacement field is constructed using the traceless normal ray integrals.

scholarly journals On a Question of Bourgain about Geometric Incidences

2008 ◽  
Vol 17 (4) ◽  
pp. 619-625 ◽  
Author(s):  
JÓZSEF SOLYMOSI ◽  
CSABA D. TÓTH
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Geometric Incidences

Given a set of s points and a set of n2 lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, we show that s = Ω(n11/4). This is the first non-trivial answer to a question recently posed by Jean Bourgain.

scholarly journals Orthogonal Isomorphic Representations Of Free Groups

1956 ◽  
Vol 8 ◽  
pp. 256-262 ◽  
Author(s):  
J. De Groot
Keyword(s):  
Euclidean Space ◽  
Free Groups ◽  
Three Dimensional ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Orthogonal Matrices ◽  
Abelian Subgroups ◽  
Proper Orthogonal

1. Introduction. We consider the group of proper orthogonal transformations (rotations) in three-dimensional Euclidean space, represented by real orthogonal matrices (aik) (i, k = 1,2,3) with determinant + 1 . It is known that this rotation group contains free (non-abelian) subgroups; in fact Hausdorff (5) showed how to find two rotations P and Q generating a group with only two non-trivial relationsP2 = Q3 = I.

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2610-2628 ◽  
Author(s):  
Davood Naderi ◽  
Mehdi Tale-Masouleh ◽  
Payam Varshovi-Jaghargh
Keyword(s):  
Euclidean Space ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dimensional Euclidean Space ◽  
Grobner Basis ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

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.

Sign in / Sign up

Export Citation Format

Share Document