An Etymological Dictionary of the German Language/rutschen
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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.’