{"id":3192,"date":"2026-03-10T22:12:49","date_gmt":"2026-03-10T21:12:49","guid":{"rendered":"https:\/\/solveredu.com\/?p=3192"},"modified":"2026-03-10T22:12:55","modified_gmt":"2026-03-10T21:12:55","slug":"kozpontos-vs-altalanos-erorendszer","status":"publish","type":"post","link":"https:\/\/solveredu.com\/hu\/post\/zbiezny-vs-dowolny-rozbiezny-uklad-sil\/","title":{"rendered":"Konvergens vs. divergens (elt\u00e9r\u0151) er\u0151rendszer - K\u00fcl\u00f6nbs\u00e9gek \u00e9s sz\u00e1m\u00edt\u00e1si m\u00f3dszerek"},"content":{"rendered":"<h2 class=\"wp-block-heading has-medium-font-size\">Hogyan hagyjuk abba a mechanika elleni harcot? Saj\u00e1t\u00edtsd el az energiarendszereket egyszer \u00e9s mindenkorra!<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A m\u00e9rn\u00f6ki tanulm\u00e1nyok \u00e1lland\u00f3 harcot jelentenek a vektorokkal, a mechanikai kollokviumok pedig r\u00e9m\u00e1lomszer\u0171ek lehetnek. A legnagyobb probl\u00e9ma? Gyakran \u00f6sszekeverj\u00fck az er\u0151rendszerek t\u00edpusait, ami m\u00e1r az elej\u00e9n rossz egyenletekhez vezet. Ma lebontjuk a dolgot, \u00e9s megmutatjuk, hogyan k\u00f6nny\u00edtheted meg a dolgodat.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"#zbiezny\"><strong>Konvergens vagy \u00f6nk\u00e9nyes? Meg kell k\u00fcl\u00f6nb\u00f6ztetni a kett\u0151t!<\/strong><\/a><\/li>\n\n\n\n<li><a href=\"#warunki\"><strong>Az egyens\u00faly felt\u00e9telei - hol a k\u00fcl\u00f6nbs\u00e9g?<\/strong><\/a><\/li>\n\n\n\n<li><a href=\"#przykladowe\"><strong>P\u00e9ld\u00e1k a feladatokra<\/strong><\/a><\/li>\n<\/ol>\n\n\n\n<h3 id=\"zbiezny\" class=\"wp-block-heading\">1. konvergens vagy \u00f6nk\u00e9nyes? Meg kell k\u00fcl\u00f6nb\u00f6ztetni a kett\u0151t!<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Miel\u0151tt a sz\u00e1m\u00edt\u00e1sokhoz l\u00e1tna, helyesen kell oszt\u00e1lyoznia a rendszer\u00e9t. Ez hat\u00e1rozza meg, hogy h\u00e1ny egyenletet kell fel\u00edrnod, \u00e9s hogy sz\u00e1mol\u00e1si pillanatokkal kell-e szemben\u00e9zned.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u00d6sszefut\u00f3 er\u0151rendszerek:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Lapos konverg\u00e1l\u00f3 er\u0151rendszer<\/strong> - A mechanik\u00e1ban a s\u00edkbeli konvergens er\u0151rendszer olyan rendszer, amelyben minden er\u0151vektor egy ir\u00e1nyban hat. <strong>egy rep\u00fcl\u0151g\u00e9p<\/strong>, \u00e9s a vonalaik (ir\u00e1nyaik) pontosan metszik egym\u00e1st a <strong>egy pont<\/strong>. Minden egyes csom\u00f3pontot pontosan \u00fagy tekint\u00fcnk, mint konvergens er\u0151k s\u00edkbeli rendszer\u00e9t.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A konverg\u00e1l\u00f3 er\u0151k t\u00e9rbeli elrendez\u00e9se<\/strong> - Egy merev testre hat\u00f3 er\u0151k olyan rendszere, amelyek hat\u00e1sir\u00e1nyai a k\u00f6vetkez\u0151 pontokban metszik egym\u00e1st <strong>egy pont<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Tetsz\u0151leges (elt\u00e9r\u0151) er\u0151k elrendez\u00e9se:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ez egy olyan helyzet, amelyben az er\u0151k sz\u00e9tsz\u00f3r\u00f3dnak. M\u0171veleti vonalaiknak nincs egyetlen \u00e9rintkez\u00e9si pontja. Egy ilyen rendszer nem csak felfel\u00e9, lefel\u00e9 vagy oldalra k\u00e9pes mozgatni a testet, hanem mindenekel\u0151tt - -. <strong>okozhat forgalmat<\/strong>. Egy ilyen rendszer lehet s\u00edkbeli, amikor az \u00f6sszes er\u0151 egy s\u00edkban helyezkedik el, vagy t\u00e9rbeli, amikor az er\u0151k k\u00fcl\u00f6nb\u00f6z\u0151 s\u00edkokban helyezkednek el.<\/li>\n<\/ul>\n\n\n\n<h3 id=\"warunki\" class=\"wp-block-heading\">2 Egyens\u00falyi felt\u00e9telek - hol a k\u00fcl\u00f6nbs\u00e9g?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Att\u00f3l f\u00fcgg\u0151en, hogy melyik rendszerrel van dolgunk, a megfelel\u0151 sz\u00e1m\u00fa egyenletet kell fel\u00edrnunk. Egy konvergens er\u0151rendszer akkor van egyens\u00falyban, ha az er\u0151vektorok egy <strong>z\u00e1rt soksz\u00f6g<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><td><strong>Jellemz\u0151<\/strong><\/td><td><strong>Konvergens rendszer<\/strong><\/td><td><strong>Elrendez\u00e9s B\u00e1rmilyen<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>Lapos<\/strong><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math>   <br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math>   <math data-latex=\"\\sum M_o = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>o<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_o = 0<\/annotation><\/semantics><\/math> <\/td><\/tr><tr><td><strong>T\u00e9rbeli<\/strong><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math> <br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_z = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>z<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_z = 0<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math>     <math data-latex=\"\\sum M_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_x = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math>     <math data-latex=\"\\sum M_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_y = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_z = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>z<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_z = 0<\/annotation><\/semantics><\/math>     <math data-latex=\"\\sum M_z = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>z<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_z = 0<\/annotation><\/semantics><\/math><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Egy s\u00edkbeli tetsz\u0151leges rendszerben egy harmadik egyenlet is szerepet kap - a kiv\u00e1lasztott ponthoz viszony\u00edtott nyomat\u00e9kok \u00f6sszege. Itt k\u00f6vetj\u00fck el a legt\u00f6bb hib\u00e1t, amikor elfelejtj\u00fck a nyomat\u00e9k ir\u00e1ny\u00e1t vagy az er\u0151 karj\u00e1t.<\/p>\n\n\n\n<h4 id=\"przykladowe\" class=\"wp-block-heading\">3 P\u00e9lda feladatok<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Az al\u00e1bbiakban egy p\u00e9ld\u00e1t tal\u00e1l egy konverg\u00e1l\u00f3 er\u0151rendszerrel ell\u00e1tott feladatra.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1215\" height=\"903\" data-attachment-id=\"2953\" data-permalink=\"https:\/\/solveredu.com\/hu\/zad2_en\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?fit=1215%2C903&amp;ssl=1\" data-orig-size=\"1215,903\" data-comments-opened=\"1\" data-image-title=\"zad2_en\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?fit=1024%2C761&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=1215%2C903&#038;ssl=1\" alt=\"\u00d6sszefut\u00f3 er\u0151rendszer, mintafeladat, Solveredu\" class=\"wp-image-2953\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?w=1215&amp;ssl=1 1215w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=300%2C223&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=1024%2C761&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=768%2C571&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=16%2C12&amp;ssl=1 16w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><figcaption class=\"wp-element-caption\"><em>Konvergens <em>lapos <\/em>er\u0151egyens\u00faly<\/em><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1217\" height=\"890\" data-attachment-id=\"2952\" data-permalink=\"https:\/\/solveredu.com\/hu\/zad1_en\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?fit=1217%2C890&amp;ssl=1\" data-orig-size=\"1217,890\" data-comments-opened=\"1\" data-image-title=\"zad1_en\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?fit=1024%2C749&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=1217%2C890&#038;ssl=1\" alt=\"B\u00e1rmilyen er\u0151rendszer, mintafeladat, Solveredu\" class=\"wp-image-2952\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?w=1217&amp;ssl=1 1217w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=300%2C219&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=1024%2C749&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=768%2C562&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=16%2C12&amp;ssl=1 16w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><figcaption class=\"wp-element-caption\"><em>B\u00e1rmilyen s\u00edk er\u0151rendszer<\/em><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A s\u00edkbeli er\u0151rendszerek feladatainak megold\u00e1s\u00e1t az ingyenes eszk\u00f6z\u00f6mben gyakorolhatja <a href=\"https:\/\/solveredu.com\/hu\/kalkulator-plaskiego-ukladu-sil\/\" data-type=\"page\" data-id=\"2945\"><strong>Lapos er\u0151 sz\u00e1mol\u00f3g\u00e9p <\/strong><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A fenti p\u00e9ld\u00e1kat ebben a programban s\u00edkbeli er\u0151rendszerek megold\u00e1s\u00e1ra gener\u00e1ljuk, ahol egy er\u0151rendszer ered\u0151je \u00e9s f\u0151nyomat\u00e9ka sz\u00e1m\u00edthat\u00f3.<\/p>","protected":false},"excerpt":{"rendered":"<p>Jak przesta\u0107 walczy\u0107 z mechanik\u0105? Opanuj uk\u0142ady si\u0142 raz a dobrze! Studia techniczne to nieustanna walka z wektorami, a kolokwia z mechaniki potrafi\u0105 \u015bni\u0107 si\u0119 po nocach. Najwi\u0119kszy problem? Cz\u0119sto mylimy typy uk\u0142ad\u00f3w si\u0142, co prowadzi do b\u0142\u0119dnych r\u00f3wna\u0144 ju\u017c na starcie. Dzi\u015b rozbijemy to na czynniki pierwsze i poka\u017cemy Ci, jak u\u0142atwi\u0107 sobie \u017cycie. [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":2953,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[14815,14816],"tags":[14846,14820,14845,14847],"class_list":["post-3192","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","category-wytrzymalosc-materialow","tag-belka-swobodnie-podparta","tag-rownania-rownowagi","tag-reakcje-podporowe","tag-stateczna-wyznaczalnosc"],"jetpack_publicize_connections":[],"jetpack_likes_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pg3flK-Pu","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?fit=1215%2C903&ssl=1","_links":{"self":[{"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/posts\/3192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/comments?post=3192"}],"version-history":[{"count":16,"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/posts\/3192\/revisions"}],"predecessor-version":[{"id":3232,"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/posts\/3192\/revisions\/3232"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/media\/2953"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/media?parent=3192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/categories?post=3192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/hu\/wp-json\/wp\/v2\/tags?post=3192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}