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Related Concept Videos

Angular Momentum01:21

Angular Momentum

Angular momentum characterizes an object's rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its...
Angular Momentum about an Arbitrary Axis01:11

Angular Momentum about an Arbitrary Axis

Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into the angular...
Angular Momentum: Single Particle01:10

Angular Momentum: Single Particle

Angular momentum is directed perpendicular to the plane of the rotation, and its magnitude depends on the choice of the origin. The perpendicular vector joining the linear momentum vector of an object to the origin is called the “lever arm.” If the lever arm and linear momentum are collinear, then the magnitude of the angular momentum is zero. Therefore, in this case, the object rotates about the origin such that it lies on the rim of the circumference defined by the lever arm magnitude.
The...
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Angular Momentum and Principle Axes of Inertia01:09

Angular Momentum and Principle Axes of Inertia

The concept of angular momentum for a solid structure is illustrated as the cumulative result of the cross-product of the position vector of the mass element and the cross-product of the body's angular velocity with the position vector.
To put this equation into simpler terms, it can be reconfigured using rectangular coordinates. This involves choosing an alternative set of XYZ axes that are arbitrarily inclined with respect to the reference frame. The process of deriving the rectangular...

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Related Experiment Video

Updated: Jun 16, 2026

Analyzing Mitochondrial Morphology Through Simulation Supervised Learning
12:06

Analyzing Mitochondrial Morphology Through Simulation Supervised Learning

Published on: March 3, 2023

Generative machine learning for multivariate angular simulation.

Jakob Benjamin Wessel1, Callum J R Murphy-Barltrop2,3, Emma S Simpson4

  • 1Department of Mathematics and Statistics, University of Exeter, Exeter, UK.

Extremes
|June 15, 2026
PubMed
Summary
This summary is machine-generated.

Deep learning methods like generative adversarial networks and normalizing flows effectively simulate multivariate angular variables in high dimensions. These advanced techniques outperform classical models, showing strong performance on real-world metocean data.

Keywords:
Angular simulationDeep generative modelsMultivariate extremesNeural networks

Related Experiment Videos

Last Updated: Jun 16, 2026

Analyzing Mitochondrial Morphology Through Simulation Supervised Learning
12:06

Analyzing Mitochondrial Morphology Through Simulation Supervised Learning

Published on: March 3, 2023

Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Simulating multivariate angular variables in high dimensions is crucial for analyzing complex datasets.
  • Empirical and classical parametric models like the von Mises-Fisher distribution (vMF) face limitations in flexibility and scalability with increasing dimensions.
  • Finite mixtures of vMF distributions offer improved flexibility but may require a large number of components for intricate data structures.

Purpose of the Study:

  • To introduce and evaluate deep learning approaches for simulating multivariate angular variables.
  • To compare the performance of deep learning methods against classical finite mixture models.
  • To demonstrate the applicability of these novel simulation techniques to real-world data.

Main Methods:

  • Generative adversarial networks (GANs)
  • Normalizing flows
  • Flow matching
  • Comparison with finite mixtures of von Mises-Fisher distributions

Main Results:

  • Deep learning methods show strong performance in simulating multivariate angular variables.
  • The proposed deep learning approaches offer greater flexibility and scalability compared to classical methods.
  • Successful application to a metocean dataset indicates practical utility for complex, real-world data.

Conclusions:

  • Deep learning offers a powerful and flexible alternative for simulating multivariate angular variables, especially in high-dimensional settings.
  • The developed methods provide a scalable solution that overcomes limitations of traditional statistical models.
  • These techniques are well-suited for analyzing complex structures in environmental and other scientific domains.