{"id":353236,"date":"2017-01-16T03:00:00","date_gmt":"2017-01-16T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=51a68f55788ea3ab3ad8f5ffcda68485"},"modified":"2017-01-16T03:00:00","modified_gmt":"2017-01-16T00:00:00","slug":"variational-symmetries-as-the-existence-of-ignorable-coordinates","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=353236","title":{"rendered":"Variational symmetries as the existence of ignorable coordinates"},"content":{"rendered":"<p>It is shown that given a Lagrangian for a system with a finite number of degrees of freedom, the<br \/>\nexistence of a variational symmetry is equivalent to the existence of coordinates in the extended<br \/>\nconfiguration space such that one of the coordinates is ignorable. The proof given here, which only<br \/>\nrequires multivariable calculus, provides an elementary derivation of the partial differential<br \/>\nequation that determines the variational symmetries of a given Lagrangian, which is obtained in<br \/>\ntreatises on the Lie theory of symmetries of differential equations or of variational calculus.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is shown that given a Lagrangian for a system with a finite number of degrees of freedom, the<br \/>\nexistence of a variational symmetry is equivalent to the existence of coordinates in the extended<br \/>\nconfiguration space such that one of the coordinates is&#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-353236","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\/353236","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=353236"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/353236\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=353236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=353236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=353236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}