File:Phase space of cubic potential.svg
Original file (SVG file, nominally 316 × 582 pixels, file size: 47 KB)
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Summary
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| Description |
Español: Gráfica de un potencial cúbico U=U(q) arriba y diversas trayectorias del espacio de las fases para un sistema físico que se encuentra bajo la interacción de dicho potencial abajo. Cada trayectoria se corresponde con una energía total E_i dada representada en el gráfico superior con el mismo color.
La Hamiltoniana tiene la forma H(q,p)=p^2/2m + U(q) y la energía total se conserva, aunque esta es distribuida continuamente entre energía potencial y cinética. Las flechas indican el sentido de las trayectorias conforme avanza la variable tiempo. Los asteriscos hacen referencia a puntos singulares del espacio de las fases, donde el sistema permanece siempre ya que se encuentra en equilibrio (estable el verde e inestable el morado). La línea morada que parece pasar (pero no lo hace realmente) por el asterisco del mismo color es especialmente interesante, aunque se trate de un caso ideal y no se puede ver en la naturaleza. Un sistema que avance en una trayectoria morada, acercándose al asterisco, necesitará un tiempo infinito para llegar hasta él, como se puede demostrar matemáticamente, por lo que nunca lo alcanzará. Esto es coherente matemática y físicamente, ya que las trayectorias en el espacio de las fases nunca pueden cruzarse, pues darían lugar a una situación indeterminista.English: Graph of a cubic potential U=U(q) above and several trajectories on the phase space for a physical system under the effect of the potential below. Each trajectory makes reference to a due total energy E_i, represented on the above graph with the same color.
The Hamiltonian has the form H(q,p)=p^2/2m + U(q) and the total energy is conserved, although it is distributed continuously between potential and kinetic energy. Arrows indicates how trajectories evolves when time variable goes forward. Asterisks make reference to singular points on the phase space, where systems stay forever since they'll be placed in a equilibrium position (stable for the green one and unstable for the purple one). The purple line which seems to cross through (but it doesn't it really) the asterisk of idem color is specially interesting, although it is an ideal that cannot be seen in nature. A system which goes following the purple trajectory, and going closer to the asterisk, will need and infinite amount of time for finally arriving to it, how it can be demonstrated mathematically. It is coherent mathematically and physically, since phase space trajectories cannot cross themselves, so it would causes a indeterminated scene. |
| Date | April-May 2012 |
| Source | Own work |
| Author | Daniel Molina García |
Licensing
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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The graph was made using GLE. You can found the code here and make your own ones. It was printed as eps and later corrected a bit with inkscape and converted to svg.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:14, 4 May 2012 | | 316 × 582 (47 KB) | Lalluviamola (talk | contribs) | {{Information |Description ={{es|1=Gráfica de un potencial cúbico U=U(q) arriba y diversas trayectorias del espacio de las fases para un sistema físico que se encuentra bajo la interacción de dicho potencial abajo. Cada trayectoria se correspond... |
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