Related papers: A two-runners model: optimization of running strat…
The aim of this paper is to bring a mathematical justification to the optimal way of organizing one's effort when running. It is well known from physiologists that all running exercises of duration less than 3mn are run with a strong…
Runners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout…
Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and…
In order to determine the optimal strategy to run a race on a curved track according to the lane number, we introduce a model based on differential equations for the velocity, the propulsive force and the anaerobic energy which takes into…
Our aim is to present a new model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem. We provide…
Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. Here we present a novel, minimal…
We present a mathematical model for optimizing breakaway strategies in competitive cycling, balancing power expenditure, aerodynamic drag, and crashing. Our framework incorporates probabilistic crash dynamics, allowing a cyclist's risk…
A simple model based on the maximum energy that an athlete can produce in a small time interval is used to describe the high and long jump. Conservation of angular momentum is used to explain why an athlete should run horizontally to…
In some athletic races, such as cycling and types of speed skating races, athletes have to complete a relatively long distance at a high speed in the presence of direct opponents. To win such a race, athletes are motivated to hide behind…
Objectives: Negative splitting (i.e., finishing the race faster) is a tactic commonly employed by elite marathon athletes, even though research supporting the strategy is scarce. The presence of pacers allows the main runner to run behind a…
Predicting the future performance of young runners is an important research issue in experimental sports science and performance analysis. We analyse a data set with annual seasonal best performances of male middle distance runners for a…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
In this report it is approched the Contest dynamics as mathematical theory, therefore applicable to all contest sports. Starting with the physical definition of Athlete and Couple of Athlete systems and after singling out the interaction…
This paper presents two complementary frameworks to optimize Formula 1 race strategies, jointly accounting for energy allocation, tire wear and pit stop timing. First, the race scenario is modeled using lap time maps and a dynamic tire wear…
Electric endurance racing is characterized by severe energy constraints and strong aerodynamic interactions. Determining race-winning policies therefore becomes a fundamentally multi-agent, game-theoretic problem. These policies must…
A multiplicative effects model is introduced for the identification of the factors that are influential to the performance of highly-trained endurance runners. The model extends the established power-law relationship between performance…
The mathematical model of J. Keller for predicting World Record race times, based on a simple differential equation of motion, predicted quite well the records of the day. One of its shortcoming is that it neglects to account for a…
With the advent of power-meters allowing cyclists to precisely track their power outputs throughout the duration of a race, devising optimal power output strategies for races has become increasingly important in competitive cycling. To do…
In this paper, we investigate a pursuit-evasion game in which a mobile observer tries to track a target in an environment containing obstacles. We formulate the game as an optimal control problem with state inequality constraint in a simple…
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct…