Category Archives: Euler’s equations

Geodesics of left invariant metrics on matrix Lie groups – Part 2 Conservation laws

Posted on 2017/05/26 by arkajad

In the last post, Geodesics of left invariant metrics on matrix Lie groups – Part 1,we have derived Arnold’s equation – that is a half of the problem of finding geodesics on a Lie group endowed with left-invariant metric. Suppose … Continue reading →

Posted in Euler's equations, Geometry | 2 Comments

Without goals everything is a propos of nothing

Posted on 2017/03/20 by arkajad

We are still traveling in the land of 4D butterflies made of remarkable circles such as those introduced in the note Meeting with remarkable circles three days ago. We did not travel too far during these three days, but we … Continue reading →

Posted in Attitude matrix, Dzhanibekov effect, Euler's equations, Quaternions, Stereographic projection | Leave a comment

Circles of eternal return

Posted on 2017/03/17 by arkajad

Let me recall the particular trajectory that we are discussing. In fact the particular part of this particular trajectory where the flip occurs. Click on the image to open gif animation. It will take time to load as it is … Continue reading →

Posted in Attitude matrix, Dzhanibekov effect, Euler's equations, Quaternions, Stereographic projection | 1 Comment