You see this is a right hand system. So, bow down is going to be positive pitch now, what is the equation of motion for that single degree equation of motion just like heave I am going to have here I moment of inertia of rigid body about which axis y y because we are going through the central gravity because this is my origin that we have defined now, we have defined the motion with respect to coordinate at c g. So, I y y let me write it down plus there is going to be let me write in this way this is added
it does not matter how we I calling it. So, we can call it this is cos may be plus here some beta theta see what I wrote here is exactly same for all equation of motion
this is just like m x dot dot for rotational motion you have what do we have, we have rigid body moment of inertia about the relevant axis y y. So, this is please understand rigid body a moment of inertia, it is not to be confused with I x x or I y y that you use
in hydrostatics for water plane area it is mass moment of inertia. Lots of students normally make this mistake may be for symbol or. So, because in hydrostatics
we use I x x I y y as moment of inertia water plane area this is rigid body mass moment of inertia not to be confused what so ever. This exactly the same thing added mass basically these two just like what we had earlier added moment of inertia and damping moment why we are calling moment because it is moments now not forces basically this part is that added moment force. So, this is you can say added pitch added mass in pitch and this is damping for pitch pitch damping. So, this is like pitch we we can call it this way pitch added moment of inertia mass we can call it moment of inertia and this is pitch damping and this of course, is pitch restoring moment hydrostatic restoring moments and this is of course, the pitch exciting moment exactly the same form is same everything is same the solution also will be same of course, this m theta is the amplitude and this is of course, the time. So, the full thing is the moment of inertia. So, you see if you look at that. In fact, if I did not call it the solution is just same as what we have done before exactly same there is no only the terms changed this is actually