Related papers: How to run 100 meters ?
In this article the pursuit problem of objects that moves with different accelerations and initial speeds is studied. Initially, the situation in which the escaping object moves in a straight line is considered. Under this condition, and if…
Empirical observations indicate striking similarities among locomotion in terrestrial animals, birds, and fish, but unifying physical grounds are lacking. When applied to efficient locomotion, the analytical mechanics principle of minimum…
Many university texts on Mechanics deal with the problem of the effect of the air drag force, using as example the slowing down of a parachute. Hardly no one discuss what happens when the drag force is proportional to both $u$ and $u^2$. In…
This paper proposes a variational approach to describe the evolution of organization of complex systems from first principles, as increased efficiency of physical action. Most simply stated, physical action is the product of the energy and…
Athletic training is characterized by physiological systems responding to repeated exercise-induced stress, resulting in gradual alterations in the functional properties of these systems. The adaptive response leading to improved…
At the 2005 world championships there was considerable discussion and a formal protest in the long distance race arising from a perceived advantage obtained by some athletes running together. It is shown that a statistical model presented…
Maximal accelerations are related to the existence of a minimal time for a given physical system. Such a minimal time can be either an intrinsic time scale of the system or connected to a quantum gravity induced ultraviolet cut off. In this…
A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations,…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
The objective of this work is to provide a mathematical analysis on how a Thoroughbred horse should regulate its speed over the course of a race to optimize performance. Because Thoroughbred horses are not capable of running the whole race…
A good racing strategy and in particular the racing line is decisive to winning races in Formula 1, MotoGP, and other forms of motor racing. The racing line defines the path followed around a track as well as the optimal speed profile along…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
Consider the circle $C$ of length 1 and a circular arc $A$ of length $\ell\in (0,1)$. It is shown that there exists $k=k(\ell) \in \mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds…
The Lonely Runner Conjecture asserts that if $n$ runners with distinct constant speeds run on the unit circle $\mathbb{R}/\mathbb{Z}$ starting from $0$ at time $0$, then each runner will at some time $t>0$ be lonely in the sense that she/he…
Pedestrians adjust both speed and stride length when they navigate difficult situations such as tight corners or dense crowds. They try to avoid collisions and to preserve their personal space. State-of-the-art pedestrian motion models…
Simple airtrack simulations, like those now possible with web-based 3D environments, can provide explorers of any age with experiential data sufficient to formulate their own models of motion. In particular, with a compressable spring, two…
The lonely runner conjecture, now over fifty years old, concerns the following problem. On a unit length circular track, consider $m$ runners starting at the same time and place, each runner having a different constant speed. The conjecture…
We are motivated by a problem about running: If a race was completed in an average pace of P minutes per mile, is there necessarily some mile of the race that was run in exactly P minutes? The answer is no. We explain why, and describe the…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…