{"id":272,"date":"2021-01-21T03:38:00","date_gmt":"2021-01-21T02:38:00","guid":{"rendered":"https:\/\/ramyrashad.com\/?p=272"},"modified":"2023-08-12T02:11:16","modified_gmt":"2023-08-12T01:11:16","slug":"rigid-body-dynamics","status":"publish","type":"post","link":"https:\/\/ramyrashad.com\/index.php\/2021\/01\/21\/rigid-body-dynamics\/","title":{"rendered":"Rigid Body Dynamics"},"content":{"rendered":"\n<p class=\"has-blue-color has-text-color\"><strong>This work has been published as Ch.4 of my PhD thesis.<\/strong><\/p>\n\n\n\n<p>The study of rigid body modeling is central to the mathematical theories of robotics. The topic of rigid bodies is a recurrent theme for serial and parallel rigid manipulators as well as for ground, underwater, and aerial mobile robots. In this work, we consider the problem of modeling rigid body motion in the port-Hamiltonian framework using the Lie group approach for describing rigid body kinematics.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-12.png\" alt=\"\" class=\"wp-image-487\" width=\"632\" height=\"317\" srcset=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-12.png 907w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-12-300x150.png 300w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-12-768x385.png 768w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><figcaption class=\"wp-element-caption\">Illustration of general rigid body motion as a curve on SE(3) which represents a family of homogeneous transformation matrices<\/figcaption><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"338\" src=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-13-1024x338.png\" alt=\"\" class=\"wp-image-488\" srcset=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-13-1024x338.png 1024w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-13-300x99.png 300w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-13-768x253.png 768w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-13.png 1198w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Commutative Diagram relating the Lie group SE(3) to the Lie algebra se(3) and its dual space se*(3).<\/figcaption><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"476\" src=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-14-1024x476.png\" alt=\"\" class=\"wp-image-491\" srcset=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-14-1024x476.png 1024w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-14-300x139.png 300w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-14-768x357.png 768w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-14.png 1339w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Decomposed port-Hamiltonian model describing rigid body dynamics as an interconnection of energetic modules characterizing storage of kinetic and gravitational potential energy<\/figcaption><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-15.png\" alt=\"\" class=\"wp-image-494\" width=\"673\" height=\"264\" srcset=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-15.png 853w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/image-15-300x118.png 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><figcaption class=\"wp-element-caption\">Explicit port-Hamiltonian dynamics of a rigid body<\/figcaption><\/figure><\/div>","protected":false},"excerpt":{"rendered":"<p>This work has been published as Ch.4 of my PhD thesis. The study of rigid body modeling is central to the mathematical theories of robotics. The topic of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":295,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"ub_ctt_via":"","_mi_skip_tracking":false,"footnotes":""},"categories":[10],"tags":[],"aioseo_notices":[],"featured_image_src":"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/07\/pHRigidBody-e1691802669272.png","author_info":{"display_name":"Ramy","author_link":"https:\/\/ramyrashad.com\/index.php\/author\/ramy-abdelmonemgmail-com\/"},"_links":{"self":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts\/272"}],"collection":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/comments?post=272"}],"version-history":[{"count":7,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts\/272\/revisions"}],"predecessor-version":[{"id":498,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts\/272\/revisions\/498"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/media\/295"}],"wp:attachment":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/media?parent=272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/categories?post=272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/tags?post=272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}