{"id":3638,"date":"2014-02-07T18:04:00","date_gmt":"2014-02-07T18:04:00","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=3638"},"modified":"2021-04-15T03:51:17","modified_gmt":"2021-04-15T03:51:17","slug":"walkers-in-a-rotating-frame-orbital-stability","status":"publish","type":"post","link":"https:\/\/thales.mit.edu\/bush\/index.php\/2014\/02\/07\/walkers-in-a-rotating-frame-orbital-stability\/","title":{"rendered":"Rotating frame: Orbital stability"},"content":{"rendered":"\n
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The stability of the circular orbits of a walking droplet in a rotating frame.<\/figcaption><\/figure>\n\n\n\n

We present the results of a theoretical investigation of droplets walking on a rotating vibrating fluid bath. The droplet\u2019s trajectory is described in terms of an integro-differential equation that incorporates the influence of its propulsive wave force. Predictions for the dependence of the orbital radius on the bath\u2019s rotation rate compare favourably with experimental data and capture the progression from continuous to quantized orbits as the vibrational acceleration is increased. The orbital quantization is rationalized by assessing the stability of the orbital solutions, and may be understood as resulting directly from the dynamic constraint imposed on the drop by its monochromatic guiding wave. The stability analysis also predicts the existence of wobbling orbital states reported in recent experiments, and the absence of stable orbits in the limit of large vibrational forcing.<\/p>\n\n\n\n

See paper:  Oza, Harris, Rosales & Bush (2014)<\/a><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":4629,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,3],"tags":[],"class_list":["post-3638","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydrodynamic-quantum-analogues","category-pilot-wave-hydrodynamics","entry"],"yoast_head":"\nRotating frame: Orbital stability - 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\/2014\/02\/07\/walkers-in-a-rotating-frame-orbital-stability\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rotating frame: Orbital stability - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2014\/02\/07\/walkers-in-a-rotating-frame-orbital-stability\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. 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