Poincare Section

Sampling can be done using whenevent with an action having sow with an enclosing reap around the call to ndsolve.

Poincare section. The poincaré section a powerful method introduced by poincaré for examining the motion of dynamical systems is that of a poincaré section. The rate of change for the object is determined for each intersection of its orbit with the disk as shown by p x and p2 x. The orbits which comprise the attractor cross the plane many times.

In mathematics particularly in dynamical systems a first recurrence map or poincaré map named after henri poincaré is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace called the poincaré section transversal to the flow of the system. Surface of section a surface or space of section also called a poincaré section rasband 1990 pp. For a poincaré section take an attractor and an arbitrary plane which cuts the attractor into two pieces.

Poincaré sections compute poincaré sections using ndsolve with whenevent. Plot the intersections of the orbits and the poincaré plane although only plot the intersections. A poincaré section or map the trajectory or orbit of an object x is sampled periodically as indicated by the blue disk.

7 and 93 94 is a way of presenting a trajectory in dimensional phase space in an dimensional space.