Actual motion of a Gyro, nutation. When we let go of a ryroit first fall, and at thesame time, process. Itfalls below the averageprocession line and thencomes up again, and fallsagain in the verticaldirection. The oscillationdamps out eventuallyFig.20-5.Actual motion of tip ofone has in the end theaxis of gyroscope under gravity justpure procession.after releasing axis previously held fixed
Actual motion of a Gyro, nutation • When we let go of a ryro, it first fall, and at the same time, process. It falls below the average procession line and then comes up again, and falls again in the vertical direction. The oscillation damps out eventually, one has in the end the pure procession
Static equilibrium of rigid bodyDynamical equations of rigid bodydidLcFi(e)ZZ7xF()FmmdtdtiCenterof massis at restF(e) = 0Norotation(e) = 0
Static equilibrium of rigid body c ( ) e i i dv m F dt = c ( ) e i i i dL m r F dt = Dynamical equations of rigid body Center of mass is at rest ( ) 0 e F = No rotation ( ) 0 e = 7