{"id":785,"date":"2022-04-11T15:23:53","date_gmt":"2022-04-11T13:23:53","guid":{"rendered":"https:\/\/technischemechanik.com\/?p=785"},"modified":"2022-04-11T15:23:53","modified_gmt":"2022-04-11T13:23:53","slug":"kreisel-rotierender-stab-mit-drehfeder","status":"publish","type":"post","link":"https:\/\/technischemechanik.com\/de\/2022\/04\/11\/kreisel-rotierender-stab-mit-drehfeder\/","title":{"rendered":"Kreisel: Rotierender Stab mit Drehfeder"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Herzlich Willkommen!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Das letzte Beispiel zur Kreiseldynamik ist schon eine ganze Weile her, deshalb wollen wir uns heute wieder einmal ein solches ansehen.<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Ein zylindrischer, homogener Stab (kein d\u00fcnner Stab) ist in einer rotierenden Gabel reibungsfrei drehbar gelagert und \u00fcber eine Drehfeder mit dieser verbunden. <\/p><p>Geg.: <br>homogener Stab: L\u00e4nge l, Durchmesser 2r, Masse m <br>lineare Drehfeder: Drehfederkonstante cT, vollkommen entspannt bei \u03d5=0 <br>Gabel: Winkelgeschwindigkeit \u03a9, die durch ein entsprechendes Antriebsmoment MA konstant gehalten wird. <\/p><p>Ges.: <br>*Wie gro\u00df darf \u03a9 h\u00f6chstens sein, damit der Stab f\u00fcr kleine Winkel \u03d5 eine Schwingung ausf\u00fchrt? <br>*Welchen Wert muss das Antriebsmoment MA(\u03d5) bei reibungsfreier Lagerung der Gabel annehmen. Anfangsbedingung: \u03d5=0, \u03d5\u02d9=\u03bd <\/p><p>Hinweis: Verwenden Sie die Euler&#8217;schen Kreiselgleichungen.<\/p><cite>Quelle: Aufgabe 4.4.4 (S. 42) aus P. Lugner et al., Technische Mechanik, 1992 Springer-Verlag, Wien<\/cite><\/blockquote>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"712\" height=\"774\" data-attachment-id=\"786\" data-permalink=\"https:\/\/technischemechanik.com\/de\/kreisel_2014_05_08\/\" data-orig-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/04\/kreisel_2014_05_08.jpg?fit=916%2C996&amp;ssl=1\" data-orig-size=\"916,996\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"kreisel_2014_05_08\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/04\/kreisel_2014_05_08.jpg?fit=712%2C774&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/04\/kreisel_2014_05_08.jpg?resize=712%2C774&#038;ssl=1\" alt=\"\" class=\"wp-image-786\" \/><\/figure>\n<\/div><\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Die Angabe zum Download gibt es wie gewohnt ihr hier:<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/04\/kreisel-k06.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px;\" aria-label=\"Einbettung von Einbettung von kreisel-k06..\"><\/object><a id=\"wp-block-file--media-a5c71da8-b890-4293-9fe2-be887e6e3f39\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/04\/kreisel-k06.pdf\">kreisel-k06<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/04\/kreisel-k06.pdf\" class=\"wp-block-file__button\" download aria-describedby=\"wp-block-file--media-a5c71da8-b890-4293-9fe2-be887e6e3f39\">Herunterladen<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Wie immer ist es wichtig sich anhand einer Skizze, d.h. eines Freik\u00f6rperbilds bewusst zu machen, welche Kr\u00e4fte und Momente sowie Geschwindigkeiten und Beschleunigungen im System wirken. Dann k\u00f6nnen wir hier auch schon die Euler&#8217;schen Kreiselgleichungen anschreiben, deren einzelne Terme bestimmen und in die allgemeine Form der Gleichungen einsetzen. Dadurch gelangen wir zu einem Gleichungssystem aus dem wir eine Bewegungsgleichung erhalten. Am Ende m\u00fcssen wir uns noch dar\u00fcber Gedanken machen, wann es sich bei dieser Bewegungsgleichung um eine Schwingungsgleichung handelt. All das besprechen wir wieder in voller Sch\u00f6nheit im verlinkten Video.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"712\" height=\"401\" src=\"https:\/\/www.youtube.com\/embed\/eQ2iAYZe9Ak?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=de-DE&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">S\u00e4mtliche Fragen beantworte ich wie immer sehr gerne &#8211; schreibt sie mir bitte einfach hier oder auf YouTube als Kommentar.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hat euch das Video gefallen? Dann lasst bitte ein Like hier auf dem Blog und auf YouTube da. Abonniert auch unbedingt den Kanal um kein Video mehr zu verpassen. Vielen Dank!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bis bald,<br>Markus <\/p>\n\n\n<div class=\"crowdsignal-feedback-wrapper\" data-crowdsignal-feedback=\"{&quot;feedbackPlaceholder&quot;:&quot;Sag mir bitte was dir besonders gefallen hat und was ich verbessern soll! 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Das letzte Beispiel zur Kreiseldynamik ist schon eine ganze Weile her, deshalb wollen wir uns heute wieder einmal ein solches ansehen. Ein zylindrischer, homogener Stab (kein d\u00fcnner Stab) ist in einer rotierenden Gabel reibungsfrei drehbar gelagert und \u00fcber eine Drehfeder mit dieser verbunden. Geg.: homogener Stab: L\u00e4nge l, Durchmesser 2r, Masse m lineare &hellip; <a href=\"https:\/\/technischemechanik.com\/de\/2022\/04\/11\/kreisel-rotierender-stab-mit-drehfeder\/\" class=\"more-link\"><span class=\"screen-reader-text\">Kreisel: Rotierender Stab mit Drehfeder<\/span> weiterlesen<\/a><\/p>\n","protected":false},"author":110396568,"featured_media":346,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_crdt_document":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[2602546,1145536,5004009],"tags":[129538,25466,2245662,7978,13261836,102130347,6886663,12237,750913297,35890,166867,3480,807373,40987001,2517859,750913303,947685,32590,5685069,727263877,662707,7091101,215605283,720191,10126,73726871,161115,172005,2411,122145655,3831784,14084,1121513,727213064,727213062,1097356,2722,33601,17744,21321],"class_list":["post-785","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ubungsaufgaben","category-dynamik","category-kreisel","tag-aufgabe","tag-beispiel","tag-beschleunigung","tag-bildung","tag-digitale-bildung","tag-digitaler-unterricht","tag-drehzahl","tag-dynamics","tag-dynamik","tag-featured","tag-hochschule","tag-homeschooling","tag-ingenieur","tag-ingenieurwissenschaft","tag-krafte","tag-kreisel","tag-losung","tag-lehre","tag-lernhilfe","tag-markus-orthaber","tag-maschinenbau","tag-maschinenbauingenieur","tag-mathematik-lernen","tag-mechanik","tag-physik","tag-physik-nachhilfe","tag-screencast","tag-studieren","tag-studium","tag-studyhelp","tag-tachometer","tag-technik","tag-technische-mechanik","tag-technische-mechanik-1","tag-technische-mechanik-2","tag-tm1","tag-uni","tag-universitat","tag-wissen","tag-wissenschaft"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2021\/12\/kreisel-wordpress.png?fit=512%2C512&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7UJuu-cF","jetpack-related-posts":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts\/785","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/users\/110396568"}],"replies":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/comments?post=785"}],"version-history":[{"count":3,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts\/785\/revisions"}],"predecessor-version":[{"id":790,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts\/785\/revisions\/790"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/media\/346"}],"wp:attachment":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/media?parent=785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/categories?post=785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/tags?post=785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}