{"id":368085,"date":"2017-02-21T03:00:00","date_gmt":"2017-02-21T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=6891c34be6f2d3b7cc46ad84b5d06eac"},"modified":"2017-02-21T03:00:00","modified_gmt":"2017-02-21T00:00:00","slug":"jacobis-approach-to-the-lagrange-top","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=368085","title":{"rendered":"Jacobi\u2019s approach to the Lagrange top"},"content":{"rendered":"<p>The integration of the differential equations of motion of the symmetric top, described by the Euler<br \/>\nangles as coordinates, is revisited using Jacobi\u2019s elliptic functions for the nutation angle and<br \/>\nJacobi\u2019s theta functions for the rotation \u03c8 and precession \u03d5 angles. The Hamiltonian function is<br \/>\nfirst modified, making it symmetric with three equal moments of inertia, to discover the action of<br \/>\nthe different moment of inertia just by adding only a constant angular velocity around the symmetry<br \/>\naxis of the top. Simultaneously, it becomes symmetric with respect to the action of rotation and<br \/>\nprecession on nutation, since interchange of the conjugated momenta of those angles does not modify<br \/>\nthe nutation, which is equivalent to the periodic motion of a particle in a cubic potential well.<br \/>\nThe differential equations for the angles \u03d5 and \u03c8 appear with symmetry that is simplified when<br \/>\nexpressed in terms of the sum and difference of these angles. This approach coinc&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The integration of the differential equations of motion of the symmetric top, described by the Euler<br \/>\nangles as coordinates, is revisited using Jacobi\u2019s elliptic functions for the nutation angle and<br \/>\nJacobi\u2019s theta functions for the rotation \u03c8 and&#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-368085","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\/368085","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=368085"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/368085\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=368085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=368085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=368085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}