What is the phase space?

phase space is the abstraction that physics use to visualize and study systems; Each point in this virtual space is the only possible condition of the system or one of the parts of it. These states are usually determined by a set of dynamic variables relevant to the development of the system. Physicists consider the phase space especially useful for the analysis of mechanical systems such as Pendula, planets orbiting a central star or masses connected by springs. In these contexts, the status of the object is determined by its location and speed or equivalent to its location and momentum. Phase space can also be used to study non-classical-and even nodreministic-systems, such as systems they encounter in quantum mechanics. The movement of the mass is determined by four factors: spring length, spring stiffness, mass of mass speed. Only the first and last of these changes over time, assuming that the minute changes in the gravitational force are ignored. The condition of the system is therefore only determined by the length of spring and rthe masses of matter

If someone pulls the mass down, the spring could stretch to a length of 10 inches (25.4 cm). When the mass is released, it is at rest for a moment, so its speed is 0 in/s. The condition of the system at this time can be described as (10 in, 0 in/s) or (25.4 cm, 0 cm/s).

The weight first accelerates up and then slows down when spring is compressed. The weight could stop rising when the spring is 6 inches (15.2 cm). At that moment, the mass is at rest again, so the condition of the system can be described as (6 in, 0 in/s) or (15.2 cm, 0 cm/s).

At the end points, the mass has zero speed, so that the surprise that it is the fastest half between them, where the spring length is 8 inches (20.3 cm). It could be assumed that the rate of matter at this point is 4 inches (10.2 cm/s). When passing the center on the way up, the system can be described as (8 in, 4 in/s) or (20.3 cm, 10.2 cm/s). To cEstě down the mass moves downwards, so the condition of the system at this point is (8 inches, -4 in/s) or (20.3 cm, -10.2 cm/s).

Graphs of these and other states of system experience create an ellipse showing the development of the system. Such a graph is called a phase chart. The specific trajectory through which a particular system passes is its orbit.

If the mass was downloaded further at the beginning, the character tracked in the phase space would be a larger ellipse. If the mass was released at the equilibrium point - at a point where the strength of spring precisely cancels the center of gravity - Massa would remain in place. That would be the only dot in the phase space. It can be seen that the orbit of this system is concentric ellipses.

The

Example of Mass in the spring illustrates an important aspect of mechanical systems defined by a single object: it is impossible for two paths to intersect. The variables representing the state of the building determine its future, so there can be only one way to one path from each point in its orbit. BothTherefore, they cannot walk each other. This feature is extremely useful for analyzing systems using phase space.