This article brings to light the fact that linearity is by itself a meaningful symmetry in the
\nsenses of Lie and Noether. First, the role played by that \u2018linearity symmetry\u2019 in the quadrature of
\nlinear second-order differential equations is revisited through the use of adapted variables and the
\nidentification of a conserved quantity as Lie invariant. Second, the celebrated Caldirola\u2013Kanai
\nLagrangian\u2014from which the differential equation is deducible\u2014is shown to be naturally generated by a
\nJacobi last multiplier inherited from the linearity symmetry. Then, the latter is recognised to be
\nalso a Noether one. Finally, the study is extended to higher-order linear differential equations,
\nderivable or not from an action principle. Incidentally, this work can serve as an introduction to
\nthe central question of continuous symmetries in physics and mathematics. It has the advantage of
\nbeing approachable to undergraduate students since the linearity symmetry is by its very nature
\nsufficient…<\/p>\n","protected":false},"excerpt":{"rendered":"
This article brings to light the fact that linearity is by itself a meaningful symmetry in the
\nsenses of Lie and Noether. First, the role played by that \u2018linearity symmetry\u2019 in the quadrature of
\nlinear second-order differential equations is revis…<\/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-409737","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\/409737","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=409737"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/409737\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=409737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=409737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=409737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}