{"id":440326,"date":"2017-08-16T02:00:00","date_gmt":"2017-08-15T23:00:00","guid":{"rendered":"https:\/\/www.fyysika.ee\/?guid=fb8e517656961aae392198b9d9f4a451"},"modified":"2017-08-16T02:00:00","modified_gmt":"2017-08-15T23:00:00","slug":"chaotic-or-just-complicated-ball-bouncing-down-the-stairs-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=440326","title":{"rendered":"Chaotic or just complicated? Ball bouncing down the stairs"},"content":{"rendered":"<p>The aim of this study is to investigate the bouncing dynamics of a small elastic ball on a<br \/>\nrectangular stairway and to determine if its dynamics is chaotic. We derive a simple nonlinear<br \/>\nrecursion for the coordinates of the collisions from which the type of dynamics cannot be predicted.<br \/>\nNumerical simulations indicate that stationary bouncing always sets in asymptotically, and is<br \/>\ntypically quasi-periodic. The dependence on the coefficient of restitution can be very complicated,<br \/>\nyet the dynamics is found to be nonchaotic. Only elementary mathematics is required for the<br \/>\ncalculations, and we offer a piece of user-friendly demo software on our website,<br \/>\nhttp:\/\/crnl.hu\/stairway [http:\/\/crnl.hu\/stairway] , to facilitate further understanding of this<br \/>\ncomplex phenomenon.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The aim of this study is to investigate the bouncing dynamics of a small elastic ball on a<br \/>\nrectangular stairway and to determine if its dynamics is chaotic. We derive a simple nonlinear<br \/>\nrecursion for the coordinates of the collisions from which the t&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-440326","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/440326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=440326"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/440326\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=440326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=440326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=440326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}