Mumbai University > MECH > Sem 5 > Theory Of Machines 2

Marks: 5 M

Year: Dec 2014

Pitching of the ship is usually considered to take place with simple harmonic motion.

The angular displacement θ of the axis of spin from its mean position is given by,

$θ = φ \sin w 0 t$

where $φ= \text{the maximum angle turned from the mean position.} \\\\ w0 = \text{Angular velocity of SHM} = 2π/T \\\\ T = \text{Time period}$

Angular velocity of precession,

$Wp = dθ/dt = φw0 \cos w0t$

This is maximum when cos w0 t = 1.

Therefore, maximum angular velocity of precession wp = φ w0

Gyroscopic couple

C = Iwwp = Iw (φ x 2π/T)