{"id":5248,"date":"2021-04-04T15:51:22","date_gmt":"2021-04-04T15:51:22","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=5248"},"modified":"2021-04-09T05:54:52","modified_gmt":"2021-04-09T05:54:52","slug":"the-elastochrone-rolling-on-a-bending-beam","status":"publish","type":"post","link":"http:\/\/thales.mit.edu\/bush\/index.php\/2021\/04\/04\/the-elastochrone-rolling-on-a-bending-beam\/","title":{"rendered":"Rolling on a bending beam"},"content":{"rendered":"\n<div class=\"wp-block-cover alignwide has-orange-background-color has-background-dim\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/elasto.png\" alt=\"\" class=\"wp-image-5420\" width=\"445\" height=\"265\"\/><\/figure>\n\n\n\n<p class=\"tw-text-wide has-extra-small-font-size\">We present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model based on Euler\u2013 Bernoulli beam theory is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the load trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favourably with our experimental observations in this quasi-static regime. The time taken for descent along an elastic beam, the elastochrone, is shown to exceed the classical brachistochrone, the shortest time between two points in a gravitational field.<\/p>\n\n\n\n<p class=\"tw-text-wide has-small-font-size\">See paper here:&nbsp;<a href=\"http:\/\/math.mit.edu\/~bush\/wordpress\/wp-content\/uploads\/2012\/10\/Elastochrone.pdf\">Aristoff, Clanet and Bush (2009)<\/a><\/p>\n<\/div><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":5422,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-5248","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-misc","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v16.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Rolling on a bending beam - John W. M. Bush<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/thales.mit.edu\/bush\/index.php\/2021\/04\/04\/the-elastochrone-rolling-on-a-bending-beam\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rolling on a bending beam - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2021\/04\/04\/the-elastochrone-rolling-on-a-bending-beam\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. 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