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First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
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A plane traveling due north at 180 km/h in still air was found to be 80 km off-course after 30 minutes, deviating approximately 5 degrees east of north. This deviation means the influence of a crosswind alters the plane’s intended trajectory. The actual ground path formed a diagonal, suggesting that the aircraft’s effective ground speed was reduced to 160 km/h and directed slightly to the east due to the wind.By analyzing the displacement from the intended path, the velocity contributed by the...
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Related Experiment Video

Updated: Jul 9, 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

Vector solitons in (2 + 1) dimensions.

J N Malmberg, A H Carlsson, D Anderson

    Optics Letters
    |December 8, 2007
    PubMed
    Summary

    This study explores stable vector spatial solitons, which are self-trapped optical beams, in nonlinear media. Researchers identified new families of these beams, some with unique topological properties.

    Area of Science:

    • Nonlinear optics
    • Mathematical physics

    Background:

    • Vector spatial solitons are crucial for optical beam control.
    • Understanding their formation and stability in different media is essential.

    Purpose of the Study:

    • Investigate the existence and stability of vector spatial solitons.
    • Identify families of two-mode self-trapped beams in bulk Kerr and saturable media.
    • Analyze beams with and without topological charge.

    Main Methods:

    • Analytical derivations.
    • Numerical simulations.
    • (2+1)-dimensional modeling.

    Main Results:

    • Existence of novel (2+1)-dimensional two-mode vector spatial solitons confirmed.

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    Published on: July 19, 2016

    Related Experiment Videos

    Last Updated: Jul 9, 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

    Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
    11:00

    Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

    Published on: July 19, 2016

  • Families of stable self-trapped beams identified in both Kerr and saturable media.
  • Properties of beams with and without topological charge characterized.
  • Conclusions:

    • The study successfully identified and characterized new families of vector spatial solitons.
    • Findings contribute to the understanding of light propagation and self-trapping in nonlinear optical media.
    • The results provide a foundation for potential applications in optical technologies.