Related papers: On the stability of four legged tables
Dynamic quadrupedal locomotion over rough terrains reveals remarkable progress over the last few decades. Small-scale quadruped robots are adequately flexible and adaptable to traverse uneven terrains along sagittal direction, such as…
The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Each of the six segments is a rod having the same length and uniform natural curvature. These rods are bent uniformly in the plane of…
The ordered configuration space of $n$ open unit squares in the $w$ by $h$ rectangle exhibits homological stability in the space direction. That is, for fixed $n$ and fixed homological degree $k$, once the underlying rectangle is large…
In this article we study some geometric properties of a non-trivial square tile (a non-trivial square tile is a non-constant function on a square). Consider infinitely many copies of this single square tile and cover the plane with them,…
Rotations on the circle by irrational numbers give rise to uniquely ergodic Sturm dynamical systems. We show that rotations by badly approximable irrationals have the property of fast ergodicity. It was shown recently that any Sturmian…
We consider billiards with a single cusp where the walls meeting at the vertex of the cusp have zero one-sided curvature, thus forming a flat point at the vertex. For H\"older continuous observables, we show that properly normalized Birkoff…
A pentagon in the plane with fixed side-lengths has a two-dimensional shape space. Considering the pentagon as a mechanical system with point masses at the corners we answer the question of how much the pentagon can rotate with zero angular…
When considering regularity of surfaces, it is its geometry that is of interest. Thus, the concept of geometric regularity or geometric continuity of a specific order is a relevant concept. In this paper we discuss necessary and sufficient…
For the planar four-vortex problem, we show that there are finitely many stationary configurations consisting of equilibria, rigidly translating configurations, relative equilibria (uniformly rotating configurations) and collapse…
The potential energy of a system in stable equilibrium has a minimum value. This property is used to derive a formula that is useful in determi- nation of stability of a floating body. It is found that a floating body is in stable…
This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…
We consider a rational map f:S->S of a complex projective surface together with an invariant meromorphic two form. Under a mild topological assumption on the map, we show that the zeroes of the invariant form can be eliminated by birational…
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…
Legged robots need to be capable of walking on diverse terrain conditions. In this paper, we present a novel reinforcement learning framework for learning locomotion on non-rigid dynamic terrains. Specifically, our framework can generate…
The stability of the fundamental defects of an unstretchable flat sheet is examined. This involves expanding the bending energy to second order in deformations about the defect. The modes of deformation occur as eigenstates of a…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…
In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial…
Consider an arrangement of $k$ lines intersecting the unit square. There is some minimum scaling factor so that any placement of a rectangle with aspect ratio $1 \times p$ with $p\geq 1$ must non-transversely intersect some portion of the…
We develop the basic and new tools for classifying non-side-to-side tilings of the sphere by congruent triangles. Then we prove that, if the triangle has any irrational angle in degree, such tilings are: a sequence of 1-parameter families…
The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The…