Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

727
Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
727
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

157
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
157
Symmetric Member in Bending01:07

Symmetric Member in Bending

454
In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
454
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

9.1K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
9.1K
Perpendicular-Axis Theorem01:16

Perpendicular-Axis Theorem

4.1K
The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
4.1K
Unsymmetric Bending01:18

Unsymmetric Bending

688
Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
688

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Covering Convex Bodies and the Closest Vector Problem.

Discrete & computational geometry·2022
See all related articles

Related Experiment Video

Updated: Dec 8, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.4K

Angular measures and Birkhoff orthogonality in Minkowski planes.

Márton Naszódi1, Vilmos Prokaj2, Konrad Swanepoel3

  • 1Department of Geometry, Alfréd Rényi Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary.

Aequationes Mathematicae
|September 21, 2020
PubMed
Summary

This study characterizes normed planes that support a B-measure, an angular measure on the unit circle. It defines Birkhoff orthogonality for unit vectors and explores conditions for B-measure existence.

Keywords:
Angle measureBirkhoff orthogonalityMinkowski spaceNormed spaceRadon planes

More Related Videos

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

13.0K
An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

10.8K

Related Experiment Videos

Last Updated: Dec 8, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.4K
MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

13.0K
An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

10.8K

Area of Science:

  • * Functional Analysis
  • * Geometric Measure Theory
  • * Normed Plane Geometry

Background:

  • * Birkhoff orthogonality is a geometric concept in normed spaces, generalizing orthogonality in Euclidean planes.
  • * B-measures are specialized angular measures on the unit circle with specific properties related to Birkhoff orthogonality.
  • * Previous work by Fankhänel introduced B-measures, motivating further investigation into their existence and properties.

Purpose of the Study:

  • * To characterize normed planes that admit the existence of a B-measure.
  • * To establish conditions on normed planes for the existence of this specialized angular measure.

Main Methods:

  • * Definition of Birkhoff orthogonality for unit vectors in a normed plane.
  • * Definition of a B-measure based on Birkhoff orthogonality and angular properties on the unit circle.
  • * Analysis of geometric properties of normed planes related to the unit disc and supporting lines.

Main Results:

  • * A characterization of normed planes admitting a B-measure is presented.
  • * The study identifies specific geometric conditions required for a normed plane to possess a B-measure.

Conclusions:

  • * The existence of B-measures is tied to the geometric structure of the normed plane.
  • * This work provides a deeper understanding of the relationship between geometric properties and measure theory in normed spaces.