{"id":3496,"date":"2016-03-27T01:38:00","date_gmt":"2016-03-27T01:38:00","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=3496"},"modified":"2021-04-15T03:32:31","modified_gmt":"2021-04-15T03:32:31","slug":"orbits","status":"publish","type":"post","link":"https:\/\/thales.mit.edu\/bush\/index.php\/2016\/03\/27\/orbits\/","title":{"rendered":"Circular orbits in a central force"},"content":{"rendered":"\n<div class=\"wp-block-cover alignwide has-subtle-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 is-style-twentytwentyone-border\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/03\/orbitpair2.png\" alt=\"\" class=\"wp-image-4942\" width=\"353\" height=\"311\"\/><\/figure>\n\n\n\n<p class=\"tw-text-wide has-extra-small-font-size\">We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet\u2019s horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.<\/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\/2016\/03\/Labousse-HarmOsc.pdf\">Labousse, M., Oza, A.U., Perrard, S. and Bush, J.W.M. (2016)<\/a><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":4942,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,3],"tags":[],"class_list":["post-3496","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydrodynamic-quantum-analogues","category-pilot-wave-hydrodynamics","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v16.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Circular orbits in a central force - 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\/2016\/03\/27\/orbits\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Circular orbits in a central force - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2016\/03\/27\/orbits\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. 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