Solutions of regular polygon with an inner particle for Newtonian N + 1-body problem
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2018.04.004
Abstract: Abstract In this paper, we prove that if the solution of the planar N + 1 -body problem has N bodies rotating at the vertices of a regular N -gon then the N bodies have… read more here.
Keywords: solutions regular; regular polygon; body problem; polygon inner ... See more keywords
ALTERNATING COLOURINGS OF THE VERTICES OF A REGULAR POLYGON
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972719000157
Abstract: Let $n,r,k\in \mathbb{N}$ . An $r$ -colouring of the vertices of a regular $n$ -gon is any mapping $\unicode[STIX]{x1D712}:\mathbb{Z}_{n}\rightarrow \{1,2,\ldots ,r\}$ . Two colourings are equivalent if one of them can be obtained from another… read more here.
Keywords: vertices regular; colourings vertices; mathbb; regular polygon ... See more keywords
Regular polygon central configurations of the N-body problem with general homogeneous potential
Sign Up to like & getrecommendations! Published in 2019 at "Nonlinearity"
DOI: 10.1088/1361-6544/ab130f
Abstract: In 1985, Perko and Walter showed that masses positioned at the vertices of a regular polygon forms a central configuration if and only if the masses are equal for the classical Newtonian N-body problem. In… read more here.
Keywords: body problem; polygon central; regular polygon;
Polygons of quantized vortices in Bose-Einstein condensates with a circular trap.
Sign Up to like & getrecommendations! Published in 2023 at "Physical review. E"
DOI: 10.1103/physreve.107.044215
Abstract: We consider a disk-shaped cold atom Bose-Einstein condensate with repulsive atom-atom interactions within a circular trap, described by a two-dimensional time-dependent Gross-Pitaevskii equation with cubic nonlinearity and a circular box potential. In this setup, we discuss… read more here.
Keywords: regular polygon; circular trap; trap; quantized vortices ... See more keywords
Regular Polygon Formations With Fixed Size and Cyclic Sensing Constraint
Sign Up to like & getrecommendations! Published in 2019 at "IEEE Transactions on Automatic Control"
DOI: 10.1109/tac.2019.2913701
Abstract: We propose a distributed control strategy for a team of agents to autonomously achieve a regular polygon formation with a desired size. Our strategy does not require global position measurements, common sense of orientation, or… read more here.
Keywords: formations fixed; control; polygon; polygon formations ... See more keywords
Stress Superposition Method and Mechanical Properties Analysis of Regular Polygon Membranes
Sign Up to like & getrecommendations! Published in 2021 at "Materials"
DOI: 10.3390/ma15010192
Abstract: In this paper, the stress superposition method (SSM) is proposed to solve the stress distribution of regular polygon membranes. The stress-solving coefficient and the calculation formula of arbitrary point stress of regular polygon membrane are… read more here.
Keywords: stress superposition; membrane; method; regular polygon ... See more keywords
Regular Polygon Central Configuration of the Restricted 1 + N-Body Problem
Sign Up to like & getrecommendations! Published in 2023 at "Universe"
DOI: 10.3390/universe9060254
Abstract: We consider the central configurations of the 1+N-body problem, where N bodies are infinitesimal and the remaining one body is dominant. For regular polygon central configurations, we prove that the masses of all the infinitesimal… read more here.
Keywords: body problem; polygon central; regular polygon; body ... See more keywords