{"id":1893,"date":"2019-04-02T22:27:43","date_gmt":"2019-04-03T02:27:43","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2019\/?p=1893"},"modified":"2019-04-18T11:00:34","modified_gmt":"2019-04-18T15:00:34","slug":"lecture-20-simulation-and-geometry","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2019\/2019\/04\/02\/lecture-20-simulation-and-geometry\/","title":{"rendered":"Bonus Lecture: Simulation and Geometry"},"content":{"rendered":"<div style=\"text-align: justify\">\nIn this lecture, we saw some of the geometry underlying classical mechanics and explored how understanding this geometry can lead us to well-behaved simulation algorithms. Along the way, we explored conservation laws and Noether&#8217;s theorem.<\/p>\n<p><center><br \/>\n<a href=\"http:\/\/brickisland.net\/DDGSpring2019\/wp-content\/uploads\/2019\/04\/DDG_Variational_Mechanics.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2019\/wp-content\/uploads\/2019\/04\/Screen-Shot-2019-04-02-at-10.24.42-PM-1024x590.png\" alt=\"Discrete Mechanics\" width=\"419\" height=\"243\" class=\"alignnone size-large wp-image-1898\" \/><br \/>\n<\/a><br \/>\n<\/center><\/p>\n<p>You can find a demo of the different Euler integrators applied to a pendulum <a href=\"http:\/\/www.cs.cmu.edu\/~mgillesp\/integrators\/\">here<\/a>, and you can find a demo of how they flow particles on phase space <a href=\"http:\/\/www.cs.cmu.edu\/~mgillesp\/PhaseSpace\/\">here<\/a>.\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>In this lecture, we saw some of the geometry underlying classical mechanics and explored how understanding this geometry can lead us to well-behaved simulation algorithms. Along the way, we explored conservation laws and Noether&#8217;s theorem. You can find a demo of the different Euler integrators applied to a pendulum here, and you can find a &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2019\/2019\/04\/02\/lecture-20-simulation-and-geometry\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Bonus Lecture: Simulation and Geometry&#8221;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1893","post","type-post","status-publish","format-standard","hentry","category-slides"],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1893","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/comments?post=1893"}],"version-history":[{"count":5,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1893\/revisions"}],"predecessor-version":[{"id":1963,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1893\/revisions\/1963"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/media?parent=1893"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/categories?post=1893"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/tags?post=1893"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}