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1 0x00h 691 pts
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8 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 ;)

4 Oct - 11:56 am

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

29 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!

17 Sep - 11:51 am

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

23 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. :)

6 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 !

21 Oct - 9:48 pm

Équation du challenge 52 corrigée, merci

16 Oct - 8:43 am

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

14 Oct - 8:57 pm

Barbapapou l'équation du challenge 29 a été corrigée

4 Oct - 10:30 am

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

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Contests list :: Physics :: Pendulum ODE I (51)

Summary

ID : 51
Points : 17
Validations :
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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 .
We will use one relative parameter as the oriented angle .



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 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 (between 0° and 1°) . With the small-angle approximation we can define and that leads to linearize our equation .


Your job :

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 ).

For your information, this differential equation is a second order equation, that means it includes a second derivative of the function ; and the form of this equation is .

Then using derivations you will have to find the solution in terms of speed (expression of the function ) and acceleration (expression de la function 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 in degree (between 0 et 1)

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

You will have to send back the evaluations of , and 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 in degree
Variables to send back
thetaStringchar*evaluations of the function in radian
dthetaStringchar*evaluations of the function in radian / second
ddthetaStringchar*evaluations of the function in radian / second^2