{"id":698530,"date":"2017-11-27T03:00:00","date_gmt":"2017-11-27T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=fccb95f0f7e6c835c4deb9f088a501ef"},"modified":"2017-11-27T03:00:00","modified_gmt":"2017-11-27T00:00:00","slug":"an-impacting-linear-three-body-system","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=698530","title":{"rendered":"An impacting linear three body system"},"content":{"rendered":"<p>We study a system of three identical bodies that can move freely on a horizontal track. Initially<br \/>\none body moves and two are at rest. The moving body impacts with one of the resting bodies which<br \/>\nthen impacts with the third and so on. The impacts are assumed to be characterised by a coefficient<br \/>\nof restitution. We investigate the total number of impacts, the final velocities of the bodies, and<br \/>\nthe final energy of the system in terms of the initial velocity and the coefficient of restitution.<br \/>\nThe problem, which originates from mechanics textbooks, can be analysed as a discrete dynamical<br \/>\nsystem with three degrees of freedom. The full solution is more subtle that one might expect.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study a system of three identical bodies that can move freely on a horizontal track. Initially<br \/>\none body moves and two are at rest. The moving body impacts with one of the resting bodies which<br \/>\nthen impacts with the third and so on. The impacts are &#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-698530","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\/698530","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=698530"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/698530\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=698530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=698530"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=698530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}