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

Equations of Equilibrium in Three Dimensions01:30

Equations of Equilibrium in Three Dimensions

1.4K
When analyzing structures or systems at rest, it is necessary to ensure they are in equilibrium. This is where the vector and scalar equations of equilibrium come into play. These equations are crucial in ensuring a structure is stable and will not collapse or fall apart. The vector and scalar equations of equilibrium provide a framework for analyzing the forces acting on a body.
According to the vector equations of equilibrium, the vector sum of all the external forces acting on a body must...
1.4K
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

676
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
676
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

5.6K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
5.6K
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

538
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
538
Rigid Body Equilibrium Problems - II01:21

Rigid Body Equilibrium Problems - II

7.5K
A rigid body is in static equilibrium when the net force and the net torque acting on the system are equal to zero.
Consider two children sitting on a seesaw, which has negligible mass. The first child has a mass (m1) of 26 kg and sits at point A, which is 1.6 meters (r1) from the pivot point B; the second child has a mass (m2) of 32 kg and sits at point C. How far from the pivot point B should the second child sit (r2) to balance the seesaw?
7.5K
Rigid Body Equilibrium Problems - I00:49

Rigid Body Equilibrium Problems - I

4.8K
A rigid body is said to be in static equilibrium when the net force and the net torque acting on the system is equal to zero. To solve for rigid body equilibrium problems, do the following steps.
4.8K

You might also read

Related Articles

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

Sort by
Same author

Nivolumab and Ipilimumab in Advanced Mismatch Repair-Deficient/Microsatellite Instability-High Noncolorectal Cancers: A Nonrandomized Clinical Trial.

JAMA oncology·2025
Same author

Circulating tumor DNA analysis guiding adjuvant therapy in stage II colon cancer: 5-year outcomes of the randomized DYNAMIC trial.

Nature medicine·2025
Same author

Differences in cancer clinical trial activity and trial characteristics at metropolitan and rural trial sites in Victoria, Australia.

The Australian journal of rural health·2024
Same author

Controlling Excited State Localization in Bichromophoric Photosensitizers via the Bridging Group.

Inorganic chemistry·2024
Same author

Systematic Tuning of Electronic Ground and Excited States in Donor-Acceptor Dyes; Steps toward Designer Compounds for Modern Technologies.

The journal of physical chemistry. A·2023
Same author

Investigation of the Geometric and Spectroscopic Properties of Four Twisted Triphenylpyridinium Donor-Acceptor Dyes.

The journal of physical chemistry. A·2022
Same journal

The coherent structures of EVP fluid flow past a circular cylinder.

Theoretical and computational fluid dynamics·2026
Same journal

Porous plates at incidence.

Theoretical and computational fluid dynamics·2025
Same journal

Fully convolutional networks for velocity-field predictions based on the wall heat flux in turbulent boundary layers.

Theoretical and computational fluid dynamics·2024
Same journal

General hydrodynamic features of elastoviscoplastic fluid flows through randomised porous media.

Theoretical and computational fluid dynamics·2024
Same journal

Dispersion of free-falling saliva droplets by two-dimensional vortical flows.

Theoretical and computational fluid dynamics·2022
Same journal

Towards robust data-driven reduced-order modelling for turbulent flows: application to vortex-induced vibrations.

Theoretical and computational fluid dynamics·2022
See all related articles

Related Experiment Video

Updated: Sep 17, 2025

Preparation of Free-Surface Hyperbolic Water Vortices
04:35

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

2.9K

Vortex equilibria using least-squares methods.

Samuel J Harris1, N R McDonald1

  • 1Department of Mathematics, University College London, Gower St, London, WC1E 6BT UK.

Theoretical and Computational Fluid Dynamics
|July 1, 2025
PubMed
Summary
This summary is machine-generated.

This study presents novel numerical methods for calculating vortex equilibria. These techniques accurately compute complex fluid dynamics, including vortex patches and sheets with point vortices.

Keywords:
AAA-least squaresLaplace’s equationLightning Laplace solverRational approximationVortex dynamics

More Related Videos

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

1.8K
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

8.8K

Related Experiment Videos

Last Updated: Sep 17, 2025

Preparation of Free-Surface Hyperbolic Water Vortices
04:35

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

2.9K
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

1.8K
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

8.8K

Area of Science:

  • Fluid Dynamics
  • Computational Science
  • Applied Mathematics

Background:

  • Vortex patches and sheets are fundamental structures in fluid dynamics.
  • Computing their equilibria, especially with point vortices, presents significant challenges.
  • Existing methods often lack the precision for complex configurations.

Purpose of the Study:

  • To develop and apply advanced numerical methods for computing rotating or stationary equilibria of vortex patches and sheets.
  • To extend existing techniques for solving Laplace's equation to handle Poisson's equation and matching conditions in multiple domains.
  • To explore new equilibrium solutions for complex vortex configurations.

Main Methods:

  • Leveraging series and rational approximation methods for solving Laplace's equation in the complex plane.
  • Employing least-squares fitting of boundary conditions to determine approximation coefficients.
  • Extending methods to solve Poisson's and Laplace's equations in two domains with boundary matching for vortex patches.
  • Computing streamlines and circulation density for vortex sheets.

Main Results:

  • Successfully reproduced known results for equilibrium vortex patches and sheets, validating the methods.
  • Computed new equilibrium solutions for a single straight sheet with satellite point vortices.
  • Discovered novel solutions for a three-sheeted vortex structure and steady, doubly-connected vortex layers around objects.

Conclusions:

  • The developed numerical methods are effective and accurate for computing vortex equilibria.
  • These techniques enable the discovery of new, complex fluid flow structures.
  • The study expands the capabilities for simulating vortical flows in various configurations.