{"id":302363,"date":"2016-10-17T02:00:00","date_gmt":"2016-10-16T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=fd80f4f813c89d47434f3861875bc168"},"modified":"2016-10-17T02:00:00","modified_gmt":"2016-10-16T23:00:00","slug":"stormer-problem-restricted-to-a-spherical-surface-and-the-euler-and-lagrange-tops","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=302363","title":{"rendered":"St\u00f6rmer problem restricted to a spherical surface and the Euler and Lagrange tops"},"content":{"rendered":"<p>In a recent work, Cort\u00e9s and Poza (2015 Eur. J. Phys. 36<br \/>\n[http:\/\/dx.doi.org\/10.1088\/0143-0807\/36\/5\/055009] 055009 ) analysed, in full, the dynamics of a<br \/>\ncharged particle in the field of a magnetic dipole restricted to a spherical surface with the dipole<br \/>\nat its centre. This model can be considered as the classical non-relativistic St\u00f6rmer problem on a<br \/>\nsphere. Here, we started from a Lagrangian approach: we derived the Hamilton equations of motion and<br \/>\nobserved that in this restricted case the equations can be reduced to quadratures, and they were<br \/>\nintegrated numerically. From the Hamiltonian function we found, for the polar angle, an equivalent<br \/>\none-dimensional system of a particle in the presence of an effective potential. In the present work<br \/>\nwe start from a change of variable to the cosine of the polar angle. In terms of this variable we<br \/>\nobtain an equation that turns out to be the same as the one of a particle in a quartic potential.<br \/>\nThen, we can actually&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a recent work, Cort\u00e9s and Poza (2015 Eur. J. Phys. 36<br \/>\n[http:\/\/dx.doi.org\/10.1088\/0143-0807\/36\/5\/055009] 055009 ) analysed, in full, the dynamics of a<br \/>\ncharged particle in the field of a magnetic dipole restricted to a spherical surface with the di&#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-302363","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\/302363","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=302363"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/302363\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=302363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=302363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=302363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}