An Etymological Dictionary of the German Language/rutschen
rutschen, vb., ‘to slide, glide, slip,’ from late MidHG. rütschen, ‘to glide,’ with the variant rützen. Perhaps it belongs to the same root as rütteln, rütten (zerrütten), which are based on MidHG. rütteln, rütten, ‘to shake.’