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The averaged system is shown to be an affine connection system subject to an appropriate forcing term. If the input codistribution is integrable, the subclass of systems with Hamiltonian equal to \"kinetic plus potential energy\" is closed under the operation of averaging. This result precisely characterizes when the notion of averaged potential arises and how it is related to the symmetric product of control vector fields. Finally, a notion of vibrational stabilization for mechanical systems is introduced, and sufficient conditions are provided in the form of linear matrix equality and inequality tests.<\/jats:p>","DOI":"10.1137\/s0363012999364176","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"542-562","source":"Crossref","is-referenced-by-count":160,"title":["Averaging and Vibrational Control of Mechanical Systems"],"prefix":"10.1137","volume":"41","author":[{"given":"Francesco","family":"Bullo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1029-0"},{"issue":"149","key":"R2","first-page":"0","volume":"107","author":"Agra\\vcev A.","year":"1978","journal-title":"Mat. Sb. 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