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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
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Optimal Foraging00:48

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How animals obtain and eat their food is called foraging behavior. Foraging can include searching for plants and hunting for prey and depends on the species and environment.
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Collisions in Multiple Dimensions: Introduction01:05

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Masking and Demasking Agents01:19

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EDTA titrations may necessitate masking and demasking agents to temporarily protect a particular metal ion in a mixture from the EDTA reaction. These agents facilitate the sequential analysis of the metal ions by forming stable complexes with some—but not all—metal ions during certain steps.
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Elastic Collisions: Case Study01:15

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Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
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Predators consume prey for energy. Predators that acquire prey and prey that avoid predation both increase their chances of survival and reproduction (i.e., fitness). Routine predator-prey interactions elicit mutual adaptations that improve predator offenses, such as claws, teeth, and speed, as well as prey defenses, including crypsis, aposematism, and mimicry. Thus, predator-prey interactions resemble an evolutionary arms race.
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Video Experimental Relacionado

Updated: Jan 17, 2026

A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
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Estrategia de Captura Distribuida en Juegos Heterogéneos de Persecución-Evasión Multiagente

Ran Shi, Hai-Tao Zhang, Jun Wang

    IEEE transactions on cybernetics
    |January 14, 2026
    PubMed
    Resumen

    Este estudio presenta un nuevo marco para juegos multiagente de persecución-evasión, que permite a los perseguidores cooperativos capturar eficazmente a los evadidos manteniendo un equilibrio de Nash. La estrategia garantiza la captura exitosa y la estabilidad de la dinámica del juego.

    Palabras clave:
    juegos multiagente de persecución-evasiónteoría de juegos cooperativosequilibrio de Nashecuaciones HJIcontrol de robots

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    Área de la Ciencia:

    • Robótica
    • Teoría de Juegos
    • Sistemas de Control

    Sus antecedentes:

    • Los juegos multiagente de persecución-evasión (MPE) implican interacciones complejas entre múltiples agentes.
    • Resolver estos juegos analíticamente es un desafío debido a las ecuaciones Hamilton-Jacobi-Isaacs (HJI) acopladas y la necesidad de un equilibrio de Nash.
    • Los métodos existentes pueden no abordar completamente la dinámica de agentes heterogéneos y las estrategias de captura cooperativa.

    Objetivo del estudio:

    • Proponer un marco de juego novedoso para problemas MPE heterogéneos colectivos.
    • Garantizar la captura cooperativa de los evadidos por los perseguidores.
    • Lograr un equilibrio de Nash en el juego MPE.

    Principales métodos:

    • Desarrollo de un marco de juego MPE cooperativo.
    • Derivación de condiciones suficientes para la capturabilidad y el equilibrio de Nash.
    • Utilización de ecuaciones Hamilton-Jacobi-Isaacs (HJI) acopladas dentro del marco.
    • Realización de simulaciones numéricas para su validación.

    Principales resultados:

    • El marco propuesto resuelve eficazmente las ecuaciones HJI acopladas en juegos MPE heterogéneos.
    • Se derivaron condiciones suficientes que garantizan tanto la capturabilidad como el equilibrio de Nash.
    • Las simulaciones numéricas confirmaron la efectividad de la estrategia de juego MPE.

    Conclusiones:

    • El marco de juego desarrollado proporciona una solución viable para problemas MPE heterogéneos colectivos.
    • La estrategia garantiza la captura cooperativa y logra el equilibrio de Nash deseado.
    • Esta investigación contribuye al avance de la teoría de juegos MPE y sus aplicaciones.