7 papers
Elastic Curves via Geometric Mechanics
Oliver Gross, Rohit Jammula, Albert Chern
Elastic curves are the mathematical shapes of thin elastic rods in equilibrium, with deep connections to mechanics, geometry, and computer graphics. Traditionally described as stat…
Vakonomic Fluids
Ritoban Roy-Chowdhury, Mohammad Sina Nabizadeh, Oliver Gross +2
We introduce a novel discretization of the incompressible Euler equations based on their interpretation as geodesic equations on the Lie group of volume-preserving diffeomorphisms.…
(Semi-)Invariant Curves from Centers of Triangle Families
Klara Mundilova, Oliver Gross
We study curves obtained by tracing triangle centers within special families of triangles, focusing on centers and families that yield (semi-)invariant triangle curves, meaning tha…
Sub--Riemannian boundary value problems for Optimal Geometric Locomotion
Oliver Gross, Florine Hartwig, Martin Rumpf +1
We propose a geometric model for optimal shape-change-induced motions of slender locomotors, e.g., snakes slithering on sand. In these scenarios, the motion of a body in world coor…
A variational approach to geometric mechanics for undulating robotic locomotion
Sean Even, Patrick S. Martinez, Cora Keogh +3
Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to f…
Elastic Curves with Variable Bending Stiffness
Oliver Gross, Ulrich Pinkall, Moritz Wahl
We study stationary points of the bending energy of curves subject to constraints on the arc-length and the curve's holonomy while simultaneously allo…
Force-Free Fields are Conformally Geodesic
Albert Chern, Oliver Gross
In this paper, we establish an equivalence between force-free fields and conformally geodesic fields, and between harmonic fields and conformally eikonal fields in the context of c…