Mechanics of floating bodies

Area of Science:

• Fluid dynamics
• Solid mechanics
• Hydrostatics

Background:

• Archimedes' principle and buoyancy are foundational to fluid mechanics.
• Standard equilibrium theories often assume simplified body geometries.
• Understanding the stability of floating bodies is crucial in naval architecture and engineering.

Purpose of the Study:

• To develop and analyze a mechanical system for rigid bodies of constant density in a calm incompressible fluid.
• To investigate the statics and dynamics of floating convex bodies.
• To establish conditions for the stability of floating rigid bodies.

Main Methods:

• Formulation of a mechanical system for rigid body dynamics and statics.
• Analysis of equilibria for convex bodies, avoiding assumptions beyond convexity.
• Application of Lyapunov stability theory.

Main Results:

• The study introduces a mechanical system for floating rigid bodies.
• It demonstrates that convex bodies can be analyzed without assuming higher regularity.
• A key finding is the Lyapunov stability of equilibria meeting a metacentric criterion-equivalent condition.

Conclusions:

• The developed mechanical system provides a rigorous framework for studying floating bodies.
• The results confirm the stability of equilibria under specific geometric and physical conditions.
• This work extends classical hydrostatics with modern stability analysis techniques.