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12THIFTOMMWORLDCONGRESS,BESANONFRANCE,JUNE1821,2007REVEALINGOFINDEPENDENTOSCILLATIONSINPLANETARYREDUCERGEAROWINGTOITSSYMMETRYLBANAKHYUFEDOSEEVMECHANICALENGINEERINGRESEARCHINSTITUTEOFRUSSIANACADEMYOFSCIENCESMOSCOW,RUSSIAABSTRACTTHEPLANETARYREDUCER11GEARISASYMMETRICSYSTEMFORITSOSCILLATIONANALYSISTHEREISAPPLIEDTHESYMMETRYGROUPREPRESENTATIONTHEORY,WHICHWASGENERALIZEDFORMECHANICALSYSTEMSITWASFOUNDTHATDUETOREDUCERSYMMETRYTHEOSCILLATIONSDECOMPOSITIONHASARISENTHEREAREINDEPENDENTOSCILLATIONSCLASSES,SUCHASANGULAROSCILLATIONSOFSOLARGEARANDEPICYCLESATELLITESOSCILLATIONSINPHASE；TRANSVERSALOSCILLATIONSOFSOLARGEARANDEPICYCLESATELLITESOSCILLATIONSINANTIPHASESOLARGEARANDEPICYCLEOSCILLATIONSINAPHASEDONOTDEPENDONANGULARSATELLITESOSCILLATIONSKEYWORDSPLANETARYREDUCER,SYMMETRY,GROUPREPRESENTATIONTHEORY,INDEPENDENTOSCILLATIONSIINTRODUCTIONITISWELLKNOWNTHATATTHEOPERATIONOFPLANETARYREDUCERTHEREAREOSCILLATIONSOFITSELEMENTS,SUCHASSOLARGEAR,EPICYCLEANDSATELLITESTHISFACTORESSENTIALLYWORSENSAQUALITYOFREDUCER’OPERAT
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