{"id":744,"date":"2021-12-12T17:27:34","date_gmt":"2021-12-12T16:27:34","guid":{"rendered":"https:\/\/blogs.ugr.es\/physics-zip\/?p=744"},"modified":"2021-12-12T17:33:16","modified_gmt":"2021-12-12T16:33:16","slug":"bases-vectoriales-curvilineas","status":"publish","type":"post","link":"https:\/\/blogs.ugr.es\/physics-zip\/bases-vectoriales-curvilineas\/","title":{"rendered":"Bases vectoriales curvil\u00edneas"},"content":{"rendered":"<p>En un espacio curvil\u00edneo coordenado (<em>u\u00b9<\/em>, <em>u\u00b2<\/em>, <em>u\u00b3<\/em>) es posible definir dos bases vectoriales en el punto (<em>q\u00b9<\/em>, <em>q\u00b2<\/em>, <em>q\u00b3<\/em>):<\/p>\n<ul>\n<li>vectores <em>tangentes<\/em> a las l\u00edneas (<em>u\u00b9<\/em>, <em>cte<\/em>, <em>cte<\/em>), (<em>cte<\/em>, <em>u\u00b2<\/em>, <em>cte<\/em>),\u00a0(<em>cte<\/em>, <em>cte<\/em>, <em>u\u00b3<\/em>) que concurren en (<em>q\u00b9<\/em>, <em>q\u00b2<\/em>, <em>q\u00b3<\/em>)<\/li>\n<li>vectores <em>perpendiculares<\/em> a los planos <em>u\u00b9<\/em>=<em>cte<\/em>,\u00a0<em>u\u00b2<\/em>=<em>cte<\/em> y\u00a0<em>u\u00b3=cte\u00a0<\/em>que se cortan en\u00a0(<em>q\u00b9<\/em>, <em>q\u00b2<\/em>, <em>q\u00b3<\/em>)<\/li>\n<\/ul>\n<p>Estos vectores no coinciden por lo general.\u00a0A estas bases se las conoce como covariante y contravariante, respectivamente. Es posible normalizar estos vectores para que no tengan dimensiones f\u00edsicas y se puedan usar para definir <em>componentes<\/em> vectoriales o tensoriales <em>f\u00edsicas<\/em>.\u00a0Para coordenadas ortogonales con bases ortonormales, las componentes covariante, contravariante y\u00a0f\u00edsicas son id\u00e9nticas.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>En un espacio curvil\u00edneo coordenado (u\u00b9, u\u00b2, u\u00b3) es posible definir dos bases vectoriales en el punto (q\u00b9, q\u00b2, q\u00b3): vectores tangentes a las l\u00edneas (u\u00b9, cte, cte), (cte, u\u00b2, cte),\u00a0(cte, cte, u\u00b3) que concurren en (q\u00b9, q\u00b2, q\u00b3) vectores perpendiculares a los planos u\u00b9=cte,\u00a0u\u00b2=cte y\u00a0u\u00b3=cte\u00a0que se cortan en\u00a0(q\u00b9, q\u00b2, q\u00b3) Estos vectores no coinciden [&hellip;]<\/p>\n","protected":false},"author":524,"featured_media":0,"comment_status":"open","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":[16,11],"tags":[],"class_list":{"0":"post-744","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-maths","7":"category-fieldtheory","8":"entry"},"_links":{"self":[{"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/posts\/744","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/users\/524"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/comments?post=744"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/posts\/744\/revisions"}],"predecessor-version":[{"id":747,"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/posts\/744\/revisions\/747"}],"wp:attachment":[{"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/media?parent=744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/categories?post=744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugr.es\/physics-zip\/wp-json\/wp\/v2\/tags?post=744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}