A planar problem in the burning of an aerosol of a unitary fuel in a closed region

1986 ◽  
Vol 26 (6) ◽  
pp. 851-857
Author(s):  
P. B. Vainshtein ◽  
Yu. A. Morgunov ◽  
R. I. Nigmatulin
Keyword(s):  
Planar Problem ◽  
Closed Region ◽  
Unitary Fuel

Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Theoretical Orientation ◽  
Robotic Manipulators ◽  
Stewart Platform ◽  
Closed Region ◽  
Leg Length ◽  
Fixed Frame ◽  
Cartesian Space ◽  
Orientation Workspace

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough–Stewart platform with given leg length ranges [ρimin,ρimax]. By use of the roll-pitch-yaw angles (ϕ,θ,ψ), the theoretical orientation workspace at a prescribed position P0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space Oϕθψ. As all rotations R(x,ϕ), R(y,θ), and R(z,ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.

Natural convection of a dusty gas in a plane closed region

1994 ◽  
Vol 65 (5) ◽  
pp. 1058-1063
Author(s):  
G. M. Makhviladze ◽  
O. I. Melikhov ◽  
E. B. Soboleva
Keyword(s):  
Natural Convection ◽  
Dusty Gas ◽  
Closed Region

scholarly journals Very-High-Eccentricity Librations at Some Higher Order Resonances

1992 ◽  
Vol 152 ◽  
pp. 153-158 ◽  
Author(s):  
J.C. Klafke ◽  
S. Ferraz-Mello ◽  
T. Michtchenko
Keyword(s):  
Phase Space ◽  
Numerical Integration ◽  
Higher Order ◽  
Planar Problem ◽  
High Eccentricity ◽  
Disturbing Potential ◽  
Numerical Exploration ◽  
Numerical Integrations ◽  
Short Period ◽  
Very High

Motions near the 3:1, 4:1 and 5:2 resonances with Jupiter are studied by means of numerical integrations of a semi-analytically averaged Sun-Jupiter-asteroid planar problem. In order to have a model including the very-high-eccentricity regions of the phase space, we adopted a set of local expansions of the disturbing potential, adequate to perform the numerical exploration of regions in the phase space with eccentricities higher than 0.9 (Ferraz-Mello and Klafke, 1991). Individual solutions and qualitative results thus obtained are completely reproduced by numerical integration of the complete equations by filtering off the short-period components of these solutions.

A Census of Planar Triangulations

1962 ◽  
Vol 14 ◽  
pp. 21-38 ◽  
Author(s):  
W. T. Tutte
Keyword(s):  
Finite Number ◽  
Interior Point ◽  
Simple Closed Curve ◽  
Closed Curve ◽  
Closed Region ◽  
Straight Segments

Let P be a closed region in the plane bounded by a simple closed curve, and let S be a simplicial dissection of P. We may say that S is a dissection of P into a finite number α of triangles so that no vertex of any one triangle is an interior point of an edge of another. The triangles are ‘'topological” triangles and their edges are closed arcs which need not be straight segments. No two distinct edges of the dissection join the same two vertices, and no two triangles have more than two vertices in common.

Unsteady 2-D Compressible Flow in Unbounded Domain

1995 ◽  
Vol 117 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Deguan Wang ◽  
E. Benjamin Wylie
Keyword(s):  
Experimental Data ◽  
Open Space ◽  
Flow Model ◽  
Subsonic Flow ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Closed Region ◽  
Open Domain ◽  
Isentropic Flow ◽  
Two Dimensional Flow

An unsteady isentropic flow model is presented to calculate the two-dimensional flow field in an arbitrarily closed region or in an open fluid domain. In the open domain, a unique boundary condition is implemented to simulate the infinite character of the open space. The characteristics-like method presented herein is shown to be robust over the entire subsonic flow range and, with the implementation of the infinite boundary, provides numerical results in agreement with analytic solutions and experimental data.

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