Is this mathematical model valid for any inclination angle of any floating body

heeling angle trimangle https://imgtu.com/i/X66jqf

θ is heeling angle，ψ is trimangle， G is weight， C is the center of buoyancy

 

For very small inclinations, let's say less than 1 or 2 degrees (this is debatable), it can be valid. For higher inclinations, these formulas represent a simplification that, for the regulatory bodies, could be unacceptable.

 

For the regulatory bodies, is there a satisfactory calculation method？

 

Of course, there are several applications (not all of them, far from it) that perform these calculations with sufficient accuracy.

 

What principles are used？The shapes of marine structures are different.

 

the principle of archimedes, always, and the balance between weights and buoyancy ;
sum of forces = 0,
sum of moments = 0

 

The shape of the underwater part is complex, the position of the buoyancy center is difficult to determine

 

Yes, those things usually happen.

 

What is the theoretical method to solve the centroid of irregular body?

 

I don't know the theoretical method, the practical one, one of them, consists of tracing various sections, for example transversals, calculating the area and centroid of each of them and performing an integration of them within the limits of the body in question.

 

I found your talk most illuminating.