Based　on　the　Timoshenko　beam　theory,　a　novel　mathematical　model　of　a　rotating　shaft　with　centrifugal　terms　is　developed　by　using　Hamilton＇s　principle　and　Euler　angles.　The　associated　conventional　model　is　provided　for　comparison　purpose.　The　features　of　the　proposed　mathematical　model　are　discussed　based　on　some　selected　coordinate　systems.　The　frequencies　and　modes　are　investigated　to　show　the　influences　of　centrifugal　terms　on　the　stability　of　the　gyroscopic　systems.　The　results　show　that　the　novel　model　proposed　may　lose　stability　due　to　the　centrifugal　terms.　It　is　also　found　that　the　backward　precession　mode　can　be　changed　into　a　forward　one　beyond　the　critical　rotating　velocity.