Mechanics of floating bodies

@article{Beig2021MechanicsOF,
  title={Mechanics of floating bodies},
  author={Robert Beig and Bernd Schmidt},
  journal={Proceedings. Mathematical, Physical, and Engineering Sciences},
  year={2021},
  volume={477}
}
  • R. Beig, B. Schmidt
  • Published 23 July 2021
  • Mathematics
  • Proceedings. Mathematical, Physical, and Engineering Sciences
We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes, allows bodies with vertices and edges, we assume the bodies to be convex and take care not to assume more regularity than that implied by convexity. One main result is the (Lyapunov) stability of equilibria satisfying a condition equivalent to the standard… 
View on Royal Society
royalsocietypublishing.org

References

SHOWING 1-10 OF 37 REFERENCES
Floating rigid bodies: a note on the conservativeness of the hydrostatic effects
Within the framework of Lagrangian mechanics, the conservativeness of the hydrostatic forces acting on a floating rigid body is proved. The representation of the associated hydrostatic potential is…
Static Equilibria of Rigid Bodies: Dice, Pebbles, and the Poincare-Hopf Theorem
By appealing to the Poincare-Hopf Theorem on topological invariants, we introduce a global classification scheme for homogeneous, convex bodies based on the number and type of their equilibria. We…
Towards a Completion of Archimedes' Treatise on Floating Bodies
On the motion of floating bodies. I
We shall restrict ourselves here to floating bodies without any means of propelling themselves. The body may, of course, be a ship lying dead in the water, but there is no real limitation to…
Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 1: Prisms
The equilibrium configurations of solid prisms of square and equilateral triangular cross section floating in a liquid are examined. It is found that these bodies float in different symmetrical or…
Neutrally Floating Objects of Density ½ in Three Dimensions
This paper is concerned with the Floating Body Problem of S. Ulam: the existence of objects other than the sphere, which can float in liquid in any orientation. Despite recent results of F. Wegner…
On bodies floating in equilibrium in every direction
Ulam's problem 19 from the Scottish Book asks: {\it is a solid of uniform density which floats in water in every position necessarily a sphere?} We obtain several results related to this problem.
Ulam floating bodies
TLDR
A new construction of bodies from a given convex body in R which are isomorphic to (weighted) floating bodies are studied, showing that these bodies are related to Ulam’s long-standing floating body problem which asks whether Euclidean balls are the only bodies that can float, without turning, in any orientation.
Differential Equations, Dynamical Systems, and Linear Algebra
Completing Book II of Archimedes’s On Floating Bodies
ConclusionOne need only glance at Archimedes’s Proposition 8 above to see thatOn Floating Bodies is several orders of magnitude more sophisticated than anything else found in ancient mathematics. It…
...
...