Homoclinic Cycles

* Türkçesi için

The homoclinic cycle term is just inspired from mathematicly similarity of homocilinic orbit definition. In mathematics, a homoclinic orbit is a trajectory of a flow of a dynamical system which joins a saddle equilibrium point to itself. More precisely, a homoclinic orbit lies in the intersection of the stable manifold and the unstable manifold of an equilibrium. Maybe not literally, but, quite similar with this definition, some trajectories in CR3BP also make a flow (or cycles) which joins an equilibrium point. Such as show in below; if a trajectory make a periodic motion around a equlibirium point then fall around to M2 (so Moon) and make 1 or more than one turn, but after that it again joins the same periodic motion around equlibirium point, then it is called Homoclinic Cycles. Also alternativly, trajectories may make a motion around equlibirium point for just one or half turn, then fall around to M2 (so Moon) and make 1 or more than one turn, but after that it again joins the same periodic motion around equlibirium point, then it may be called “quasi-Homoclinic Cycles”. If they joins two different equilibrium points, then they are called Heterocilinic Cycles. These cycles can be very promising and adventageous for various science orbits.

Some examples;

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s