{"id":1616,"date":"2015-10-22T06:05:23","date_gmt":"2015-10-22T04:05:23","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1616"},"modified":"2015-10-29T07:25:36","modified_gmt":"2015-10-29T05:25:36","slug":"centro-de-masas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/centro-de-masas\/","title":{"rendered":"Centro de masas"},"content":{"rendered":"<p>El centro de masas de un sistema discreto es el punto geom\u00e9trico que din\u00e1micamente se comporta como si en \u00e9l estuviera aplicada la resultante de las fuerzas externas al sistema.<\/p>\n<p>Representamos un conjunto de n masas en el plano mediante una lista de n pares de la forma ((a(i),b(i)),m(i)) donde (a(i),b(i)) es la posici\u00f3n y m(i) la masa puntual. Las coordenadas del centro de masas (a,b) se calculan por<\/p>\n<pre lang=\"text\">\n   a = (a(1)*m(1) + a(2)*m(2) + ... + a(n)*m(n)) \/ (m(1) + m(2) +...+ m(n))\n   b = (b(1)*m(1) + b(2)*m(2) + ... + b(n)*m(n)) \/ (m(1) + m(2) +...+ m(n))\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   centrodeMasas :: [((Float,Float),Float)] -> (Float,Float) \n<\/pre>\n<p>tal que (centrodeMasas xs) es las coordenadas del centro<br \/>\nde masas del sistema discreto xs. Por ejemplo:<\/p>\n<pre lang=\"text\">\n   centrodeMasas [((-1,3),2),((0,0),5),((1,3),3)] == (0.1,1.5)\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n (por comprensi\u00f3n):\ncentrodeMasas :: [((Float,Float),Float)] -> (Float,Float) \ncentrodeMasas xs = \n    (sum [a*m | ((a,_),m) <- xs] \/ t,\n     sum [b*m | ((_,b),m) <- xs] \/ t)\n    where t = sum [m | (_,m) <- xs]\n\n-- 2\u00aa definici\u00f3n (por recursi\u00f3n):\ncentrodeMasas2 :: [((Float,Float),Float)] -> (Float,Float)\ncentrodeMasas2 xs = aux xs (0,0,0)\n    where aux [] (as,bs,ms)             = (as\/ms, bs\/ms)\n          aux (((a,b),m):ys) (as,bs,ms) = aux ys (as+a*m,bs+b*m,ms+m)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El centro de masas de un sistema discreto es el punto geom\u00e9trico que din\u00e1micamente se comporta como si en \u00e9l estuviera aplicada la resultante de las fuerzas externas al sistema. Representamos un conjunto de n masas en el plano mediante una lista de n pares de la forma ((a(i),b(i)),m(i)) donde (a(i),b(i)) es la posici\u00f3n y&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[4],"tags":[8],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1616"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=1616"}],"version-history":[{"count":9,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1616\/revisions"}],"predecessor-version":[{"id":1656,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1616\/revisions\/1656"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}