{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/45606"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/45606","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Dynamics of an unbalanced ring spinning on a rough horizontal surface","abstract":"An interesting stability property, as fascinating as that of spinning tops and gyroscopes, is observable in the motion of an unbalanced ring spinning on a rough horizontal surface. An analytical and numerical study is performed to investigate the general motion of an unbalanced ring modeled as a thin ring with a particle attached to its rim. The translational motion is represented by the rectangular coordinates of the ring geometric center. The rotational motion is represented by a 1-2-3 set of Euler angles. The kinetic motion equations are derived with the use of Newton's second law and Euler's rotational motion equations. The types of motion considered are the pure-rolling and rolling-with-slipping motions. Given favorable initial conditions, ring properties, and a sufficiently large constraint force in the form of friction, the ring undergoes a pure-rolling motion. For other conditions, however, limitations on the magnitude of the friction force render the pure the mathematical model to allow switching from pure-rolling to rolling-with-slipping motion and vice versa. The general motions of the unbalanced ring, obtained by numerically integrating the governing equations with the use of the seventh-eighth order Runge-Kutta method, are in very good qualitative agreement to those observed during an experiment performed with the use of a high-speed video camera.","abstract_html":"An interesting stability property, as fascinating as that of spinning tops and gyroscopes, is observable in the motion of an unbalanced ring spinning on a rough horizontal surface. An analytical and numerical study is performed to investigate the general motion of an unbalanced ring modeled as a thin ring with a particle attached to its rim. The translational motion is represented by the rectangular coordinates of the ring geometric center. The rotational motion is represented by a 1-2-3 set of Euler angles. The kinetic motion equations are derived with the use of Newton's second law and Euler's rotational motion equations. The types of motion considered are the pure-rolling and rolling-with-slipping motions. Given favorable initial conditions, ring properties, and a sufficiently large constraint force in the form of friction, the ring undergoes a pure-rolling motion. For other conditions, however, limitations on the magnitude of the friction force render the pure the mathematical model to allow switching from pure-rolling to rolling-with-slipping motion and vice versa. The general motions of the unbalanced ring, obtained by numerically integrating the governing equations with the use of the seventh-eighth order Runge-Kutta method, are in very good qualitative agreement to those observed during an experiment performed with the use of a high-speed video camera.","abstract_has_math":false,"creators":["Budiman, Benny S."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Kraige, Luther Glenn"],"committee_members":["Heller, Robert A.","Ragab, Saad A."],"year":1993,"date_issued":"1993-04-08","date_published":"1993-04-08","updated_at":"2026-07-22T22:19:48Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-11102009-020140"],"render_values":[{"text":"etd-11102009-020140","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/45606","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Kraige, Luther Glenn"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Heller, Robert A.","Ragab, Saad A."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Budiman, Benny S."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:49:24Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:49:24Z","2009-11-10"]},{"key":"dc:date.issued","label":"Date","values":["1993-04-08"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-11102009-020140"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/45606"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["An interesting stability property, as fascinating as that of spinning tops and gyroscopes, is observable in the motion of an unbalanced ring spinning on a rough horizontal surface. An analytical and numerical study is performed to investigate the general motion of an unbalanced ring modeled as a thin ring with a particle attached to its rim. The translational motion is represented by the rectangular coordinates of the ring geometric center. The rotational motion is represented by a 1-2-3 set of Euler angles. The kinetic motion equations are derived with the use of Newton's second law and Euler's rotational motion equations. The types of motion considered are the pure-rolling and rolling-with-slipping motions. Given favorable initial conditions, ring properties, and a sufficiently large constraint force in the form of friction, the ring undergoes a pure-rolling motion. For other conditions, however, limitations on the magnitude of the friction force render the pure the mathematical model to allow switching from pure-rolling to rolling-with-slipping motion and vice versa. The general motions of the unbalanced ring, obtained by numerically integrating the governing equations with the use of the seventh-eighth order Runge-Kutta method, are in very good qualitative agreement to those observed during an experiment performed with the use of a high-speed video camera."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Dynamics of an unbalanced ring spinning on a rough horizontal surface"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Kraige, Luther Glenn"],"dc:contributor.committeemember":["Heller, Robert A.","Ragab, Saad A."],"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Budiman, Benny S."],"dc:date.accessioned":["2014-03-14T21:49:24Z"],"dc:date.available":["2014-03-14T21:49:24Z","2009-11-10"],"dc:date.issued":["1993-04-08"],"dc:description.abstract":["An interesting stability property, as fascinating as that of spinning tops and gyroscopes, is observable in the motion of an unbalanced ring spinning on a rough horizontal surface. 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