Related papers: Simple Model of a Standing Vertical Jump
Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in velocity and potentials of acceleration; the equation system consists of a single vector equation and potentials updates. The…
We have proposed a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the…
We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate $N=\mathcal{O}(10^6)$ particles or more. As a first application we consider a dense…
Precise perception of contact interactions is essential for fine-grained manipulation skills for robots. In this paper, we present the design of feedback skills for robots that must learn to stack complex-shaped objects on top of each other…
If a tennis ball is held above a basket ball with their centers vertically aligned, and the balls are released to collide with the floor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple…
We study random walk with unbounded jumps in random environment. The environment is stationary and ergodic, uniformly elliptic and decays polynomially with speed $Dj^{-(3+\varepsilon_0)}$ for some small $\varepsilon_0>0$ and proper $D>0.$…
Robots operating in domestic environments generally need to interact with articulated objects, such as doors, cabinets, dishwashers or fridges. In this work, we present a novel, probabilistic framework for modeling articulated objects as…
We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy ``piston'', with elastic collisions between particles but inelastic collisions between the light particles and the interval…
Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly $b$ children, with $b \ge 3$. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
We introduce a toy model of the "rat race" in which individuals try to better themselves relative to the rest of the population. An individual is characterized by a real-valued fitness and each advances at a constant rate by an amount that…
This paper presents two novel approaches to solve the classic simple harmonic motion. In one approach, the distance between the equilibrium position and the maximal displacement is divided into N equal segments. In each segment, the mass…
Using an experimental optimization approach, this study investigated whether two human movements, pointing tasks and squat-jumps, could be modelled with a reduced set of kinematic parameters. Three sigmoid models were proposed to model the…
Experimental evidence is presented connecting small fluctuations in the posture of a quiet standing subject and the probability that the subject will have an accidental fall within a time period of one year. The data can be understood on…
To understand the process of pattern formation in a low-density granular flow, we propose a simple particle model. This model considers spherical particles moving over an inclined flat surface based on three forces: gravity as the driving…
Physical reasoning is a core aspect of intelligence in animals and humans. A central question is what model should be used as a basis for reasoning. Existing work considered models ranging from intuitive physics and physical simulators to…
We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of…
We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…
Estimating the metric height of a person from monocular imagery without additional assumptions is ill-posed. Existing solutions either require manual calibration of ground plane and camera geometry, special cameras, or reference objects of…
We propose an elementary proof based on a penalization technique to show the existence and uniqueness of the solution to a system of variational inequalities modelling the friction-based motion of a two-body crawling system. Here for each…