Inthispaper,weprovethatforholonomicnonconservativedynamicalsystemthePoincareandPoincaré-Cartanintegralinvariantsdonotexist.Insteadofthem,weintroducetheintegralvariantsofPoincaréCartan’stypeandofPoincaré’stypeforholonomienoneonservativedynamicalsystems,andusethesevariantstosolvetheproblemofnonlinearvibration.Wealsoprovethattheintegralinvariantsintro-ducedinreferences[1]and[2]aremerelythebasicintegralvariantsgivenbythispaper.
