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The first studies of these systems go back over a century, but a comprehensive understanding of their dynamics is still missing. The system has an $$\\mathrm {SO(3)}\\times \\mathrm {SO(2)}$$<\/jats:tex-math>\n \n \n SO<\/mml:mi>\n (<\/mml:mo>\n 3<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n \u00d7<\/mml:mo>\n \n SO<\/mml:mi>\n (<\/mml:mo>\n 2<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> symmetry and reduces to four dimensions. We extend in various directions, particularly from the case $$\\Omega =0$$<\/jats:tex-math>\n \n \u03a9<\/mml:mi>\n =<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to the case $$\\Omega \\not =0$$<\/jats:tex-math>\n \n \u03a9<\/mml:mi>\n \u2260<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, a number of previous results and give new results. In particular, we prove that the reduced system is Hamiltonizable even if $$\\Omega \\not =0$$<\/jats:tex-math>\n \n \u03a9<\/mml:mi>\n \u2260<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and, exploiting the recently introduced \u201cmoving energy,\u201d we give sufficient conditions on the profile of the surface that ensure the periodicity of the reduced dynamics and hence the quasiperiodicity of the unreduced dynamics on tori of dimension up to three. Furthermore, we determine all the equilibria of the reduced system, which are classified in three distinct families, and determine their stability properties. In addition to this, we give a new form of the equations of motion of nonholonomic systems in quasi-velocities which, at variance from the well-known Hamel equations, use any set of quasi-velocities and explicitly contain the reaction forces.<\/jats:p>","DOI":"10.1007\/s00332-022-09842-5","type":"journal-article","created":{"date-parts":[[2022,9,11]],"date-time":"2022-09-11T15:02:23Z","timestamp":1662908543000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Dynamics of a Heavy Symmetric Ball that Rolls Without Sliding on a Uniformly Rotating Surface of Revolution"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3632-1661","authenticated-orcid":false,"given":"Marco","family":"Dalla Via","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1043-3152","authenticated-orcid":false,"given":"Francesco","family":"Fass\u00f2","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3963-8581","authenticated-orcid":false,"given":"Nicola","family":"Sansonetto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,11]]},"reference":[{"key":"9842_CR1","unstructured":"Abbena, E., Salamon, S., Gray, A.: Modern Differential Geometry of Curves and Surfaces with Mathematica\u00ae, 3d edn. 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