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

Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

1.5K
Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
1.5K
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
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

525
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
525
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

669
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.
669
Conservation of Linear Momentum for a System of Particles01:28

Conservation of Linear Momentum for a System of Particles

251
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
251

You might also read

Related Articles

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

Sort by
Same author

Tunable In-Plane Anomalous Hall and Magneto-Optical Kerr Effects via Stacking Engineering in Two-Dimensional Magnets.

Nano letters·2025
Same author

Domain-Selective 1D Moiré Engineering and Topological Transitions in Bilayer Graphene.

Nano letters·2025
Same author

Medication abortion and procedural abortion in the second trimester: Comparison of complications at 16-23 6/7 Weeks' gestation.

European journal of obstetrics, gynecology, and reproductive biology·2025
Same author

Minimally Invasive Treatment of Abdominal Pregnancy Implanted on the Ileocecal Junction.

Journal of minimally invasive gynecology·2024
Same author

Exploring Muslim Women's Reproductive Health Needs and Preferences in the Emergency Department.

The western journal of emergency medicine·2023
Same author

Switching the Moiré Lattice Models in the Twisted Bilayer WSe<sub>2</sub> by Strain or Pressure.

Nano letters·2023
Same journal

Novel Parent Survey Measures Sensory Behaviors Incorporating Sensory Modality and Stimulus Intensity.

Heliyon·2026
Same journal

Expression of concern: "SQSTM1/p62 promotes the progression of gastric cancer through epithelial-mesenchymal transition" [Heliyon 10 (2024) e24409].

Heliyon·2026
Same journal

Expression of concern: "TL1A promotes metastasis and EMT process of colorectal cancer" [Heliyon 10 (2024) e24392].

Heliyon·2026
Same journal

Expression of concern: "Factors affecting timing of surgery following neoadjuvant chemoradiation for esophageal cancer" [Heliyon 9 (2023) e23212].

Heliyon·2026
Same journal

Expression of concern: "On stratified single-valued soft topogenous structures" [Heliyon 10 (2024) e27926].

Heliyon·2026
Same journal

Expression of concern: "Artifact removal and motor imagery classification in EEG using advanced algorithms and modified DNN" [Heliyon 10 (2024) e27198].

Heliyon·2026
See all related articles

Related Experiment Video

Updated: Jul 22, 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

Conserved quantities of Euler-Lagrange system via complex Lagrangian.

M Umar Farooq1, Anum Naseem2, C Wafo Soh3

  • 1Department of Basic Sciences & Humanities, College of E & ME, National University of Sciences and Technology (NUST), H-12, Islamabad, Pakistan.

Heliyon
|July 24, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a complex Lagrangian technique to find more conserved quantities for Euler-Lagrange systems. The method yields 10 Noether-like operators and conserved quantities, surpassing previous findings.

Keywords:
Conserved quantityEuler-Lagrange systemNoether-like operator

More Related Videos

Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

9.0K
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

8.6K

Related Experiment Videos

Last Updated: Jul 22, 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
Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

9.0K
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

8.6K

Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • Classical Mechanics

Background:

  • Euler-Lagrange (EL) systems are fundamental in classical mechanics.
  • Existing methods identify Noether and Lie conserved quantities.
  • Previous studies by Fang et al. and Nucci expanded on conserved quantities for EL systems.

Purpose of the Study:

  • To introduce a novel complex Lagrangian technique for deriving Noether-like operators and conserved quantities.
  • To demonstrate that previously identified conserved quantities can be obtained using this complex variational formalism.
  • To uncover additional conserved quantities beyond those previously reported.

Main Methods:

  • Application of complex Lagrangian formalism.
  • Derivation of Noether-like operators.
  • Identification of associated conserved quantities (first integrals).

Main Results:

  • The complex Lagrangian technique successfully generates 10 Noether-like operators and 10 corresponding invariant quantities for EL systems.
  • Three specific conserved quantities (Noether, Lie, Mei) identified by Fang et al. are reproduced.
  • Several other conserved quantities align with those reported by Nucci, with additional novel ones discovered.

Conclusions:

  • The complex variational formalism provides an effective alternative approach for computing invariant quantities in EL systems.
  • This methodology expands the number of known conserved quantities for these systems.
  • The findings offer new insights into the symmetries and conservation laws of Euler-Lagrange systems.