Top 20

 1 0x00h 691 pts 2 boris39 691 pts 3 thefinder 691 pts 4 neoxquick 672 pts 5 maf-ia 654 pts 6 eax 653 pts 7 nikokks 610 pts 8 benito255 600 pts 9 mego 584 pts 10 madbat2 575 pts 11 plucth 557 pts 12 Mart 545 pts 13 rostale 544 pts 14 Stupefy 525 pts 15 tehron 510 pts 16 Kithyane 493 pts 17 egosum 466 pts 18 malose 423 pts 19 CoYoTe99 412 pts 20 Undr 408 pts

Full ranking

Shoutbox

metatr0n8 Oct - 10:01 am

Salut nikokks Ce problème n'est pas évident en effet. Une manière de faire est de trouver les formes les plus simples, et de les "effacer" de l'image avant de chercher les formes plus complexes ;)

nikokks4 Oct - 11:56 am

Salut a tous =) , je bug sur le problème 28 (forme analysis). Quelqu'un aurait il une piste ?

thefinder29 Sep - 5:38 pm

Coucou oui, tu peux m'envoyer un mail si tu veux. Le plus simple, ce serait d'avoir un package pour python 3. J'ai essayé et ça n'a pas marché!

metatr0n17 Sep - 11:51 am

Salut thefinder, ça faisait longtemps ! Oula ça en fait des problèmes :'( Le premier challenge ? La somme de deux nombres ?

thefinder23 Jul - 2:13 am

Coucou, j'ai essayé de reprendre avec python. J'ai plusieurs soucis. 1) Il faut rajouter headers={'Content-Type': 'application/x-www-form-urlencoded'} avec un requests.session(). 2) Je n'ai pas réponse du serveur si je soumet une réponse au premier challenge. J'essaye finir en python les 3 dernières épreuves qui me reste. :)

Grolaf6 Nov - 8:17 am

Bonjour, un léger problème sur l'épreuve 10 : Une fois réussie, le champ "points earned" indique 72 au lieu de 7 En revanche sur le site le nombre de points comptabilisés est bien 7 Merci pour ce site génial !

Eisenheim21 Oct - 9:48 pm

Équation du challenge 52 corrigée, merci

rostale16 Oct - 8:43 am

Bonjour, il y a aussi un problème d'affichage "invalid equation" dans le challenge 52. Merci

Eisenheim14 Oct - 8:57 pm

Barbapapou l'équation du challenge 29 a été corrigée

Barbapapou4 Oct - 10:30 am

Bonjour, il y a un problème avec l'affichage d'une équation dans le challenge 29

Support usx

 You like µContest ? Support us by voting (fun and difficulty) for µContest on WeChall :) If you have not already, take the opportunity to link your Wechallaccount to µContest in order to be able to vote ! Thank you

Summary

 ID : 51 Points : 17 Validations : Challenge page Report a bug

Description

This challenge is the first of a series about resolution of nonlinear differential equations.

A nonlinear differential equation is a nonlinear equation that relates some function with its derivatives.

For this kind of equation, there are often no analytical solutions; hence, numerical methods are required to solve these equations. These methods will be the purpose of these challenges.

First, we want to consider a simple physical system which leads to a nonlinear differential equation: the simple gravity pendulum.

We will model this system with a rigid bar (OA) with length l and no mass ; we will place a punctual mass m at the end A of the bar. Pivot link in O is supposed as a perfect one (frictionless). Gravity field is $\vec g = g\vec {x_0}$.
We will use one relative parameter $\theta (t)$ as the oriented angle $(\vec{x_0},\vec{OA})$.

We want to solve the equation of motion of this system, which is a nonlinear differential equation. More precisely, as this equation of motion and the function $\theta (t)$ and its derivatives have only one independent variable (the time t), we have a particular kind of equations named ordinary differential equations or ODE.

In order to see if numerical results are corrects, first we want to find a way to linearize our ODE. Hence we can have an analytical solution as a ‘reference’ one.

So the goal of this challenge is to solve the equation of motion of the system, with a small initial angle $\theta_0$ (between 0° and 1°) . With the small-angle approximation we can define $\cos\theta = 1$ and $\sin\theta = \theta$ that leads to linearize our equation .

Once you have determined the linearized equation of motion of the system (there is a big amount of documentation about the subject on the internet), you will have to solve it (using an analytical way) in order to find the solution in terms of position of the problem (expression of the function $\theta(t)$).

For your information, this differential equation is a second order equation, that means it includes a second derivative of the function $\theta(t)$ ; and the form of this equation is $\ddot\theta(t)=G(\theta(t))$.

Then using derivations you will have to find the solution in terms of speed (expression of the function $\dot\theta(t)$) and acceleration (expression de la function $\ddot\theta(t)$ of the problem.

In order to solve this challenge, you will get two variables that define dimensions and initial conditions of the system:

l : length of the bar in meter
theta_0 : initial angle $\theta_0$ in degree (between 0 et 1)

We give g = 9.81m.s-2 , m = 5kg and $\dot\theta_0$ (initial rotationnal speed)= 0deg.s-1 .

You will have to send back the evaluations of $\theta(t)$ , $\dot\theta(t)$ and $\ddot\theta(t)$ for t = 0 , 1 , 2 , 3 , 4 , 5, 6, 7, 8, 9, 10 seconds , each value will be truncated at 5 decimals.
Hence, 4.56657946 will lead to 4.56657, -56.254886 will lead to -56.25488 et 0.12 will lead to 0.12000 .

Example

l = 1.15
theta_0 = 0.75

theta = "-0.01277;0.01183;-0.01031;0.00830;-0.00588;0.00317;-0.00032;-0.00255;0.00530;-0.00779"
dtheta = "-0.00837;0.01634;-0.02352;0.02955;-0.03415;0.03708;-0.03822;0.03749;-0.03495;0.03070"
ddtheta = "0.10894;-0.10094;0.08802;-0.07083;0.05020;-0.02712;0.00273;0.02179;-0.04525;0.06652"

Variables

Name Type Description
Variables to get
lRealfloatbar lenght in meter
theta_0Realfloatinitial angle $\theta_0$ in degree
Variables to send back
thetaStringchar*evaluations of the function $\theta(t)$ in radian
dthetaStringchar*evaluations of the function $\dot\theta(t)$ in radian / second
ddthetaStringchar*evaluations of the function $\ddot\theta(t)$ in radian / second^2