**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Flattening

Summary

Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes and of the resulting ellipse or ellipsoid is
The compression factor is in each case; for the ellipse, this is also its aspect ratio.
There are three variants: the flattening sometimes called the first flattening, as well as two other "flattenings" and each sometimes called the second flattening, sometimes only given a symbol, or sometimes called the second flattening and third flattening, respectively.
In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flattenings are zero for a circle (a = b).
{| class="wikitable" style="border:1px solid darkgray;" cellpadding="5"
! style="padding-left: 0.5em" scope="row" | (First) flattening
| style="padding-left: 0.5em" |
| style="padding-left: 0.5em" |
| style="padding-left: 0.5em " | Fundamental. Geodetic reference ellipsoids are specified by giving
|-
! style="padding-left: 0.5em" scope="row" | Second flattening
| style="padding-left: 0.5em" |
| style="padding-left: 0.5em" |
| style="padding-left: 0.5em" | Rarely used.
|-
! style="padding-left: 0.5em" scope="row" | Third flattening
| style="padding-left: 0.5em" |
| style="padding-left: 0.5em" |
| style="padding-left: 0.5em" | Used in geodetic calculations as a small expansion parameter.
|}
The flattenings can be related to each-other:
The flattenings are related to other parameters of the ellipse. For example,
where is the eccentricity.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related people (1)

Related courses (3)

Related publications (9)

Related concepts (6)

Related lectures (35)

ME-411: Mechanics of slender structures

Analysis of the mechanical response and deformation of slender structural elements.

ME-104: Introduction to structural mechanics

The student will acquire the basis for the analysis of static structures and deformation of simple structural elements. The focus is given to problem-solving skills in the context of engineering desig

ME-466: Instability

This course focuses on the physical mechanisms at the origin of the transition of a flow from laminar to turbulent using the hydrodynamic instability theory.

Earth ellipsoid

An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation.

Planetary coordinate system

A planetary coordinate system (also referred to as planetographic, planetodetic, or planetocentric) is a generalization of the geographic, geodetic, and the geocentric coordinate systems for planets other than Earth. Similar coordinate systems are defined for other solid celestial bodies, such as in the selenographic coordinates for the Moon. The coordinate systems for almost all of the solid bodies in the Solar System were established by Merton E.

Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.

Deformable Structures I: Introduction

Introduces the computation of deformations in structures by combining struts and rigid members, emphasizing equilibrium and displacement diagrams.

Shells III: Reissner's Solution

Explores Reissner's solution for shells, the DMV theory, and Zoelly's solution for pressure buckling.

Non-straight Beams: Frames and Arches

Covers the analysis of beams with concentrated loads, continuous load distributions, and matching conditions for frames and arches.

The neoclassical tearing modes (NTM) increase the effective heat and particle radial transport inside the
plasma, leading to a flattening of the electron and ion temperature and density profiles at a given location
depending on the safety factor q ration ...

2017Flattened and kinematically correlated planes of dwarf satellite galaxies have been observed in the Local Volume. The slinging out of satellites during host galaxy mergers has been suggested as a formation mechanism for these peculiar structures. We statis ...

2023Niels Quack, Teodoro Graziosi, Nathanaël Restori

The present invention concerns a layer or substrate flattening method comprising the steps of: - providing a layer or substrate (1) to be flattened; - measuring a topography or surface profile of at least one area (3) of the layer or substrate to be flatte ...

2021