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

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.6K
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...
20.6K
Vector Components in the Cartesian Coordinate System01:29

Vector Components in the Cartesian Coordinate System

31.0K
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...
31.0K
Gravitational Potential Energy for Extended Objects01:07

Gravitational Potential Energy for Extended Objects

2.1K
Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:
2.1K
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

1.5K
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
1.5K
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

1.2K
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
1.2K
Instantaneous Center of Zero Velocity01:20

Instantaneous Center of Zero Velocity

963
General plane motion, often observed in a rolling wheel, refers to a type of movement where the wheel is simultaneously rotating and translating. This complex motion can be understood by breaking it down into individual components.
To analyze this, consider two points on the wheel: point A and point B. The absolute velocity of point B can be expressed as the vector sum of the absolute velocity of point A and the relative velocity of point B with respect to point A. To simplify this analysis,...
963

You might also read

Related Articles

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

Sort by
Same author

Sustaining herd immunity against measles: Insights from a serological cohort study in an outbreak-free population.

Infection·2026
Same author

Demonstrating true disease freedom distinct from low prevalence across time: A zero inflated model with disease introduction and spread considerations.

Preventive veterinary medicine·2026
Same author

Female Mice with HSD17B1 Inactivation Show Mild Hyperandrogenism without Notable Impact on Reproductive Function or Bone.

Endocrinology·2025
Same author

Surrogate model for Bayesian optimal experimental design for adsorption isotherm parameters in chromatography.

Journal of chromatography. A·2025
Same author

A simple modification to the classical SIR model to estimate the proportion of under-reported infections using case studies in flu and COVID-19.

Infectious Disease Modelling·2024
Same author

HSD17B1 Compensates for HSD17B3 Deficiency in Fetal Mouse Testis but Not in Adults.

Endocrinology·2024

Related Experiment Video

Updated: Apr 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Generalized correlation integral vectors: A distance concept for chaotic dynamical systems.

Heikki Haario1, Leonid Kalachev2, Janne Hakkarainen3

  • 1School of Engineering Science, Lappeenranta University of Technology, Lappeenranta, Finland.

Chaos (Woodbury, N.Y.)
|June 29, 2015
PubMed
Summary

This study introduces a statistically sound method to quantify variability in chaotic dynamical systems. It uses a modified correlation integral to create a distance measure for estimating model parameters, demonstrated with Lorenz systems.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope
15:10

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope

Published on: October 9, 2014

12.0K

Related Experiment Videos

Last Updated: Apr 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope
15:10

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope

Published on: October 9, 2014

12.0K

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Computational Physics
  • Statistical Modeling

Background:

  • Fractal dimensions characterize attractors in chaotic systems, but numerical approximations are sensitive to various factors.
  • Variability in trajectory sampling affects the reliability of fractal dimension calculations.

Purpose of the Study:

  • To develop a statistically sound approach for quantifying trajectory variability in chaotic dynamical systems.
  • To introduce a novel method for estimating model parameters using a statistical distance concept.

Main Methods:

  • Modification of the correlation integral to generate a variability-summarizing vector.
  • Estimation of the distribution of this stochastic vector to define a statistical distance between trajectories.
  • Application of Markov chain Monte Carlo (MCMC) sampling for parameter estimation.

Main Results:

  • A robust statistical distance measure was developed to quantify trajectory variability.
  • The method successfully estimated model parameters for the Lorenz 63 and Lorenz 95 systems.
  • Posterior distributions of model parameters were generated using MCMC.

Conclusions:

  • The proposed statistically sound approach effectively quantifies trajectory variability in chaotic systems.
  • The developed statistical distance is a valuable tool for parameter estimation in chaotic dynamic models.
  • The methodology provides a framework for robust analysis of chaotic systems.