Related papers: A unified model for the long and high jump
When the laws of Physics are taken seriously, the sports can benefit in getting better results, as was the case of the high jump in Flop style, so that the athlete sprints diagonally towards the bar,then curve and leap backwards over it.…
In order to describe the velocity and the anaerobic energy of two runners competing against each other for middle-distance races, we present a mathematical model relying on an optimal control problem for a system of ordinary differential…
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…
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…
World records in athletics provide a measure of physical as well as physiological human performance. Here we analyse running records and show that the mean speed as a function of race time can be described by two scaling laws that have a…
Track and field world records have risen and fallen throughout the history of the sport. A recent rash of record-breaking performances has prompted the question: "How good can we get?". This article offers a review of several attempts to…
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…
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…
In this paper we use Newton's 3rd law to deduce the simplest model of an object that can perform a standing vertical jump -- a two-segmented object with an initial constant repulsive force between the segments, followed by an abrupt…
When a fluid jet strikes an inclined solid surface at normal incidence, gravity creates a flow pattern with a thick outer rim resembling a parabola and reminiscent of a hydraulic jump. There appears to be little theory or experiments…
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…
Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its…
We provide scientific foundations for athletic performance prediction on an individual level, exposing the phenomenology of individual athletic running performance in the form of a low-rank model dominated by an individual power law. We…
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…
If we know that some kind of sequence always converges, we can ask how quickly and how uniformly it converges. Many convergent sequences converge non-uniformly and, relatedly, have no computable rate of convergence. However proof-theoretic…
Because the decathlon tests many facets of athleticism, including sprinting, throwing, jumping, and endurance, many consider it to be the ultimate test of athletic ability. On this view, estimating the maximal decathlon score and…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of…
In order to clarify common assumptions on the form of energy and momentum in elasticity, a generalized conservation format is proposed for finite elasticity, in which total energy and momentum are not specified a priori. Velocity, stress,…
Performance analyses based on videos are commonly used by coaches of athletes in various sports disciplines. In individual sports, these analyses mainly comprise the body posture. This paper focuses on the disciplines of triple, high, and…