{"id":110973,"date":"2015-08-06T03:00:00","date_gmt":"2015-08-06T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=0d4452dfa96633f52b29a3af16cfb83b"},"modified":"2015-08-06T03:00:00","modified_gmt":"2015-08-06T00:00:00","slug":"expanding-the-simple-pendulums-rotation-solution-in-action-angle-variables-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=110973","title":{"rendered":"Expanding the simple pendulum&#8217;s rotation solution in action-angle variables"},"content":{"rendered":"<p>Integration of Hamiltonian systems by reduction to action-angle variables has proven to be a<br \/>\nsuccessful approach. However, when the solution depends on elliptic functions, the transformation to<br \/>\naction-angle variables may need to remain in implicit form. This is exactly the case of the simple<br \/>\npendulum, where it is shown that in order to make explicit the transformation to action-angle<br \/>\nvariables, one needs to resort to nontrivial expansions of special functions and series reversion.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Integration of Hamiltonian systems by reduction to action-angle variables has proven to be a<br \/>\nsuccessful approach. However, when the solution depends on elliptic functions, the transformation to<br \/>\naction-angle variables may need to remain in implicit fo&#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-110973","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\/110973","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=110973"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/110973\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=110973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=110973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=110973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}