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--- basic_tools:phase_space [2018/05/06 13:48]
jakobadmin [Concrete]
+++ basic_tools:phase_space [2018/11/13 22:27]
supeng_hong [Intuitive]
@@ Line 5: / Line 5: @@
 <tabbox Intuitive>
-A phase space is a mathematical tool that allows to grasp important aspects of complicated systems.
+A phase space is a mathematical tool that allows us to grasp important aspects of complicated systems.
 Each point of the phase space represents one specific configuration a given system can be in.
@@ Line 56: / Line 56: @@
 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 |}}
+<--