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

Rigid Body Equilibrium Problems - I00:49

Rigid Body Equilibrium Problems - I

5.5K
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.
5.5K
Rigid Body Equilibrium Problems - II01:21

Rigid Body Equilibrium Problems - II

8.0K
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?
8.0K
Kinetic Energy for a Rigid Body01:13

Kinetic Energy for a Rigid Body

539
Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.
539
Equation of Motion for a Rigid Body01:12

Equation of Motion for a Rigid Body

623
The movement of a rigid object can be understood through the equations that explain both translational and rotational motion about the center of mass of the object, point G. This center of mass is the point where the equation of motion for translational motion comes into play, as per Newton's Second Law.
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different...
623
Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

750
Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
Next,...
750
Angular Momentum: Rigid Body01:11

Angular Momentum: Rigid Body

15.9K
The total angular momentum of a rigid body can be calculated using the summation of the angular momentum of all the tiny particles rotating in the same plane. Considering all the tiny particles rotating in the x-y plane, the direction of angular momentum of all such particles and that of the rigid body would be perpendicular to the plane of the rotation along the z-axis.
This calculation can get complicated when tiny particles within the rigid body are not rotating in the same plane but have...
15.9K

You might also read

Related Articles

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

Sort by
Same author

Unique Geometry and Texture From Corresponding Image Patches.

IEEE transactions on pattern analysis and machine intelligence·2021
Same author

Occupational exposure to glass wool fibers: An update.

Journal of occupational and environmental hygiene·2021
Same author

Hidden symmetries generate rigid folding mechanisms in periodic origami.

Proceedings of the National Academy of Sciences of the United States of America·2020
Same author

From Shading to Local Shape.

IEEE transactions on pattern analysis and machine intelligence·2015
Same author

Periodic planar disc packings.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2014
Same author

A geometrical approach to computing free-energy landscapes from short-ranged potentials.

Proceedings of the National Academy of Sciences of the United States of America·2012
Same journal

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta.

Proceedings. Mathematical, physical, and engineering sciences·2025
Same journal

Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences.

Proceedings. Mathematical, physical, and engineering sciences·2023
Same journal

The Elbert range of magnetostrophic convection. I. Linear theory.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Soft wetting with (a)symmetric Shuttleworth effect.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

The quantum theory of time: a calculus for q-numbers.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Integrable nonlinear evolution equations in three spatial dimensions.

Proceedings. Mathematical, physical, and engineering sciences·2022
See all related articles

Related Experiment Video

Updated: Jan 28, 2026

Quantifying Corticolous Arthropods Using Sticky Traps
05:28

Quantifying Corticolous Arthropods Using Sticky Traps

Published on: January 19, 2020

5.9K

Rigidity for sticky discs.

Robert Connelly1, Steven J Gortler2, Louis Theran3

  • 1Department of Mathematics, Cornell University, Ithaca, NY, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|March 12, 2019
PubMed
Summary
This summary is machine-generated.

A packing of n discs with generic radii has at most 2n-3 contacts. Such packings exhibit rigid body motion if and only if they achieve this maximum number of contacts, revealing key combinatorial and rigidity properties.

Keywords:
circle packingsjammingrigidity

More Related Videos

The Rigid Tube as an Alternative in Controlling the Problematic Airway
08:26

The Rigid Tube as an Alternative in Controlling the Problematic Airway

Published on: June 6, 2020

6.9K
Author Spotlight: Unlocking Plant Transformation by Innovating with Carbon Nanofiber Arrays
05:32

Author Spotlight: Unlocking Plant Transformation by Innovating with Carbon Nanofiber Arrays

Published on: July 21, 2023

2.2K

Related Experiment Videos

Last Updated: Jan 28, 2026

Quantifying Corticolous Arthropods Using Sticky Traps
05:28

Quantifying Corticolous Arthropods Using Sticky Traps

Published on: January 19, 2020

5.9K
The Rigid Tube as an Alternative in Controlling the Problematic Airway
08:26

The Rigid Tube as an Alternative in Controlling the Problematic Airway

Published on: June 6, 2020

6.9K
Author Spotlight: Unlocking Plant Transformation by Innovating with Carbon Nanofiber Arrays
05:32

Author Spotlight: Unlocking Plant Transformation by Innovating with Carbon Nanofiber Arrays

Published on: July 21, 2023

2.2K

Area of Science:

  • Computational Geometry
  • Discrete Mathematics
  • Materials Science

Background:

  • Disc packings are fundamental in geometry and physics.
  • Understanding their combinatorial and rigidity properties is crucial for applications.
  • Previous work has explored limits on contacts and motion but lacked a unified framework for generic radii.

Purpose of the Study:

  • To establish an upper bound on the number of contacts in disc packings with generic radii.
  • To characterize the conditions under which such packings exhibit rigid body motion.
  • To provide a novel perspective on jamming problems in granular materials.

Main Methods:

  • Combinatorial analysis of disc-disc contacts.
  • Topological and differential geometric techniques to study the configuration space of packings.
  • Application of the Cauchy-Alexandrov stress lemma to prove manifold properties of the packing space.
  • Analysis of allowed motions preserving tangencies and disjointness.

Main Results:

  • A packing of n discs with generic radii has at most 2n-3 contacts.
  • Rigid body motion is achieved if and only if the packing has exactly 2n-3 contacts.
  • The space of packings with a fixed contact graph is a smooth manifold.
  • A finite variant of a jamming result by Connelly et al. is proven.

Conclusions:

  • The number of contacts in disc packings is tightly linked to their rigidity.
  • Generic radii simplify the analysis of packing configurations and motions.
  • The findings have implications for understanding jamming and the mechanical behavior of granular systems.