Steiner triangular drop dynamics
Abstract
Steiner's circumellipse is the unique geometric regularization of any triangle to a circumscribed ellipse with the same centroid, a regularization that motivates our introduction of the Steiner triangle as a minimal model for liquid droplet dynamics. The Steiner drop is a deforming triangle with one side making sliding contact against a planar basal support. The center of mass of the triangle is governed by Newton's law. The resulting dynamical system lives in a four dimensional phase space and exhibits a rich one-parameter family of dynamics. Two invariant manifolds are identified with "bouncing" and "rocking" periodic motions; these intersect at the stable equilibrium and are surrounded by nested quasiperiodic motions. We study the inherently interesting dynamics and also find that this model, however minimal, can capture space-time symmetries of more realistic continuum drop models.
- Publication:
-
Chaos
- Pub Date:
- February 2020
- DOI:
- 10.1063/1.5113786
- arXiv:
- arXiv:1906.04710
- Bibcode:
- 2020Chaos..30b3118W
- Keywords:
-
- Mathematics - Dynamical Systems
- E-Print:
- 23 pages, 19 figures To appear in Chaos: An Interdisciplinary Journal of Nonlinear Science, February 2020