{"id":402263,"date":"2017-04-28T02:00:00","date_gmt":"2017-04-27T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=b6262e9a6df77b9f24e7d515fbe7bf59"},"modified":"2017-04-28T02:00:00","modified_gmt":"2017-04-27T23:00:00","slug":"minimum-descent-time-along-a-set-of-connected-inclined-planes-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=402263","title":{"rendered":"Minimum descent time along a set of connected inclined planes"},"content":{"rendered":"<p>The time required for a particle to slide frictionlessly down a set of ramps connected end to end<br \/>\ncan be minimized numerically as a function of the coordinates of the connection points between ramps<br \/>\nand compared to the exact cycloidal solution of the brachistochrone problem. It is found that a set<br \/>\nof just three joined ramps over a large range of geometrical aspect ratios has a descent time within<br \/>\n5% of the optimal cycloid. The special case where the particle starts and ends at the same height<br \/>\nhas sufficient symmetry that it can be analyzed analytically using algebra alone. The level of<br \/>\nanalysis is appropriate to an undergraduate classical mechanics course.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The time required for a particle to slide frictionlessly down a set of ramps connected end to end<br \/>\ncan be minimized numerically as a function of the coordinates of the connection points between ramps<br \/>\nand compared to the exact cycloidal solution of the&#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-402263","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\/402263","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=402263"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/402263\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=402263"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=402263"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=402263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}