This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
basic_tools:phase_space [2018/05/03 13:22] jakobadmin |
basic_tools:phase_space [2018/05/12 13:27] jakobadmin [Concrete] |
||
---|---|---|---|
Line 52: | Line 52: | ||
It is conventional to say that the time evolution | It is conventional to say that the time evolution | ||
- | is governed by a flow in phase space. | + | is governed by a **flow** in phase space. |
+ | To understand this image that you follow one individual trajectory in phase space. Say, you take a pencil, put it down at one point in phase space and then start to draw the correct trajectory for the system which follows from [[equations:hamiltons_equations|Hamilton's equations]]. Now, this trajectory is only one thing that can happen in our system. When we are interested in the bigger picture, we need to follow all trajectories that are possible. This means, that we take an infinite number of pencils, put them down and the draw the trajectories. Each trajectory is calculated with Hamilton's equations. The set of all possible trajectories defines a flow in phase space. | ||
+ | |||
+ | ---- | ||
+ | |||
+ | **Examples** | ||
+ | |||
+ | -->Phase space of a harmonic oscillator# | ||
+ | {{ :basic_tools:phasespaceoscillator.png?nolink&600 |}} | ||
+ | |||
+ | <-- | ||
+ | |||
+ | -->Phase space of a pendlum# | ||
+ | |||
+ | {{ :basic_tools:phasespacependulum2.png?nolink&600 |}} | ||
+ | <-- | ||