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

Euler Equations of Motion01:19

Euler Equations of Motion

255
Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
255
Euler's Equations of Motion01:28

Euler's Equations of Motion

500
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains...
500
Equation of Motion: Rotation About a Fixed Axis01:18

Equation of Motion: Rotation About a Fixed Axis

226
Consider a flywheel, having an uneven mass distribution, rotating steadily around a fixed axis. As this rotation occurs, the center of mass of the flywheel traces a circular path. Understanding the acceleration of this center of mass requires observing both its tangential and normal components.
The tangential component is dependent on the direction of the angular acceleration of the flywheel. The tangential component of the acceleration propels the flywheel along its path. On the other hand,...
226
Equation of Motion: General Plane motion - Problem Solving01:16

Equation of Motion: General Plane motion - Problem Solving

208
Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
The friction between the roller and the ground is characterized by two coefficients. The static friction coefficient is 0.15, while the kinetic friction coefficient is 0.1. These values are crucial in understanding the interaction between...
208
Equation of Rotational Dynamics01:08

Equation of Rotational Dynamics

8.7K
Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...
8.7K
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

14.0K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
14.0K

You might also read

Related Articles

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

Sort by
Same author

Nonlinear periodic orbit solutions and their bifurcation structure at the origin of soliton hopping in coupled microresonators.

Communications physics·2026
Same author

The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation.

Chaos (Woodbury, N.Y.)·2025
Same author

Predicting chaotic statistics with unstable invariant tori.

Chaos (Woodbury, N.Y.)·2023
Same author

Invariant tori in dissipative hyperchaos.

Chaos (Woodbury, N.Y.)·2022
Same author

Fully localized post-buckling states of cylindrical shells under axial compression.

Proceedings. Mathematical, physical, and engineering sciences·2017
Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Jul 23, 2025

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

1.7K

Jacobian-free variational method for computing connecting orbits in nonlinear dynamical systems.

Omid Ashtari1, Tobias M Schneider1

  • 1Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

Chaos (Woodbury, N.Y.)
|July 17, 2023
PubMed
Summary
This summary is machine-generated.

Researchers developed a new variational method to find connecting orbits in chaotic systems. This robust technique efficiently computes complex dynamics in high-dimensional systems without Jacobian matrices.

More Related Videos

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
06:55

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling

Published on: August 5, 2016

8.2K
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.2K

Related Experiment Videos

Last Updated: Jul 23, 2025

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

1.7K
Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
06:55

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling

Published on: August 5, 2016

8.2K
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.2K

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Computational Mathematics
  • Nonlinear Dynamics

Background:

  • Spatiotemporal chaos is often described by unstable invariant sets within a system's chaotic attractor.
  • Existing numerical methods struggle to identify heteroclinic and homoclinic connections between these sets.
  • Computing connecting orbits is crucial for understanding complex dynamical systems.

Purpose of the Study:

  • To propose a novel, robust matrix-free variational method for computing connecting orbits between equilibrium solutions.
  • To overcome limitations of traditional shooting-based methods in identifying complex dynamical connections.
  • To enable the study of spatiotemporal chaos in high-dimensional systems.

Main Methods:

  • A variational approach reformulates connecting orbit identification as a minimization problem.
  • A cost function penalizes deviations of trial curves from integral curves of the vector field.
  • Adjoint-based minimization techniques are employed, avoiding explicit Jacobian matrix computation.
  • The method is demonstrated on the one-dimensional Kuramoto-Sivashinsky equation.

Main Results:

  • The proposed method successfully computes connecting orbits between equilibrium solutions.
  • It handles systems with high-dimensional unstable manifolds without limitations.
  • The approach avoids exponential error amplification common in time-marching chaotic systems.
  • Linear memory scaling allows application to high-dimensional dynamical systems.

Conclusions:

  • The matrix-free variational method offers a robust and efficient solution for computing connecting orbits.
  • This technique advances the study of spatiotemporal chaos and complex dynamics.
  • It provides a powerful tool for analyzing high-dimensional nonlinear systems.