As an example, the figure shows the flow of a damped pendulum.
The black arrows of the vector field F are tangential at the
trajectories.
In a twodimensional phase space, you can draw a qualitative
picture of the flow and the orbits. First, draw the socalled null clines.
These are the lines were the time derivative
of one component of the state variable is zero.
Here, one null cline is the angle axes because the time derivative of the angle is
zero when the angular velocity is zero.
The other null cline is =  _{0}^{2}sin/.
On these null clines, draw the vector field vertical or horizontal, respectively.
Between the null clines draw the vector field in the direction north east,
south east, south west, or north west. The direction is determined by the
signs of d/dt and d/dt. At the crossing points of the null clines, the
vector field is zero, i.e., d/dt =
0 and d/dt = 0.
These points are called fixed points.
They correspond to stationary solutions.
Fixed points are examples of nonwandering sets.
They can be either stable or unstable.
