Related papers: Simple Model of a Standing Vertical Jump
The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…
We analyze the stationary flow of a jet of Newtonian fluid that is drawn by gravity onto a moving surface. The situation is modeled by a third-order ODE on a domain of unknown length and with an additional integral condition; by solving…
Machines that can predict the effect of physical interactions on the dynamics of previously unseen object instances are important for creating better robots and interactive virtual worlds. In this work, we focus on predicting the dynamics…
Understanding physical phenomena is a key competence that enables humans and animals to act and interact under uncertain perception in previously unseen environments containing novel objects and their configurations. Developmental…
In this paper, we study the challenging problem of predicting the dynamics of objects in static images. Given a query object in an image, our goal is to provide a physical understanding of the object in terms of the forces acting upon it…
High dynamic jump motions are challenging tasks for humanoid robots to achieve environment adaptation and obstacle crossing. The trajectory optimization is a practical method to achieve high-dynamic and explosive jumping. This paper…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
We study particle hopping on a two-leg ladder where a particle can jump to their immediate neighbours, one at a time, with rates that depend on the occupation of the departure site and a neighbouring site on the other leg. For specific…
We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping…
In this paper, we study a wheeled robot with a prismatic extension joint. This allows the robot to build up momentum to perform jumps over obstacles and to swing up to the upright position after the loss of balance. We propose a template…
In this article, we propose a method for calculation of the inverse and direct dynamic models of the Orthoglide, a parallel robot with threedegrees of freedom in translation. These models are calculated starting from the elements of the…
Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…
Articulated objects (e.g., doors and drawers) exist everywhere in our life. Different from rigid objects, articulated objects have higher degrees of freedom and are rich in geometries, semantics, and part functions. Modeling different kinds…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
We prove that the only nearest neighbor jump process with local dependence on the occupation times satisfying the partial exchangeability property is the vertex reinforced jump process, under some technical conditions. This result gives a…
Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of {\it convex} axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class…
Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
The paper is devoted to the study of the motion of one-dimensional rigid bodies during a free fall in a quasi-Newtonian hyperviscous fluid at low Reynolds number. We show the existence of a steady solution and furnish sufficient conditions…
Understanding physical phenomena is a key competence that enables humans and animals to act and interact under uncertain perception in previously unseen environments containing novel object and their configurations. Developmental psychology…