Commit fc2457c8 authored by Yassine's avatar Yassine
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eazahgv

parent 3f9694ee
......@@ -53,61 +53,62 @@
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......@@ -8,23 +8,24 @@
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\documentclass[a4paper,12pt]{article}
\usepackage{lingmacros}
\usepackage{tree-dvips}
\usepackage{fancyhdr}
\usepackage{mathtools}
\usepackage[utf8]{inputenc} %encodage d'entrée
......@@ -131,8 +132,64 @@ On déduit des tableaux comparatifs ci-dessus que la masse est proportionnelle
\subsection{Semaines 2 et 3}
\subsubsection{Application du PFS pour déterminer la masse}
On cherche à déterminer la masse appliquée sur le train avant du rafale au repos. On cherchera un chargement maximal et un chargement minimal.\\
Afin de faire une estimation des efforts subits par le train avant du rafale, on cherche à déterminer la masse qui y est appliquée s au repos. On la calculera pour un chargement maximal et pour un chargement minimal.\\
Pour cela, on va commencer par isoler l’avion (1), et lister les actions qu’il subit.\\
\begin{figure}[H]
\centering
\includegraphics[scale=0.23]{images/cr1/rafale.png}
\caption{Schéma de la Rafale}
\end{figure}
-Action de la pesenteur:\\
$\overrightarrow{G_{P/1}} (G_P)= \left\{ \overrightarrow{R_P} , \overrightarrow{M_P}(G_P) \right\}$
$\overrightarrow{R_P} = -M.G\overrightarrow{y}$ ,
$\overrightarrow{M_P}(F_P) = \overrightarrow{0}$
-Action du Sol(0):\\
$\overrightarrow{G_{0/1A}} (A)= \left\{ \overrightarrow{M_{0/1A}} , \overrightarrow{M_{0/1A}}(A) \right\}$
$=$
$\begin{Bmatrix}
0 & 0\\
Y_{RA} & 0\\
0 & 0
\end{Bmatrix}$\\
$\overrightarrow{G_{0/1B}} (A)= \left\{ \overrightarrow{M_{0/1B}} , \overrightarrow{M_{0/1B}}(B) \right\}$
$=$
$\begin{Bmatrix}
0 & 0\\
Y_{RB} & 0\\
0 & 0
\end{Bmatrix}$\\
$\overrightarrow{G_{0/1O}} (O)= \left\{ \overrightarrow{M_{0/1O}} , \overrightarrow{M_{0/1O}}(O) \right\}$
$=$
$\begin{Bmatrix}
0 & 0\\
Y_{RO} & 0\\
0 & 0
\end{Bmatrix}$\\
On a ainsi exprimé la réaction sur le train avant. On peut maintenant, grâce au principe fondamental de la statique déterminer la valeur de la réaction sur le train avant.
Comme le système est immobile, on déduit que la pesanteur appliquée sur le train avant est l’opposé de la réaction. Ainsi, en divisant ce poids par la valeur de G, on obtient la masse appliquée sur le train avant du rafale lorsque l’avion est immobile.\\
\begin{equation}
\begin{cases}
Y_{RA} = Y_{RB}\\
Y_{RO} = -MG \times \frac{CG_P}{CD} + MG\\
MG = \frac{2CD.Y_{RA}}{CG_P} \iff Y_{RA} = MG \times \frac{CG_P}{2CD}
\end{cases}
\end{equation}
On peut ensuite faire l’application numérique du problème en prenant les cas d’un chargement maximal et d’un chargement minimal en faisant varier le centre de masse G et les différentes distances entre les points.\\
Echelle: 16.85cm -> 1530cm\\
Rafale sans charge maximale:\\
$$\overline{OC} = \overline{AE} = \overline{BF}$$
$$\overline{CGP} = 428cm = 4.28m$$
$$\overline{CD} = 4.812m$$
$$MG = 24500 \times 9.8 = 240100N$$
$$YR_O = -240100 \times \frac{4.28}{4.812}+ 240100 = 26545N$$
Réaction train avant = 26545$\overrightarrow{y}$
......
......@@ -7,29 +7,29 @@
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\contentsline {paragraph}{Activité 3}{11}{section*.11}%
\contentsline {paragraph}{Activité 4}{11}{section*.12}%
\contentsline {paragraph}{Activité 5}{12}{section*.13}%
\contentsline {section}{\numberline {4}Partie Mathématiques}{12}{section.4}%
\contentsline {subsection}{\numberline {4.1}Semaine 1}{12}{subsection.4.1}%
\contentsline {subsubsection}{\numberline {4.1.1}Pourquoi les systèmes vus en ZG étaient descriptibles par des équations différentielles ?}{12}{subsubsection.4.1.1}%
\contentsline {section}{\numberline {5}Partie Informatique}{13}{section.5}%
\contentsline {section}{\numberline {6}Synthèse}{15}{section.6}%
\contentsline {subsection}{\numberline {6.1}Similarités théorique (calculées lor de la première activité)}{15}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Similarités lors de l’expérimentation}{15}{subsection.6.2}%
\contentsline {section}{\numberline {7}Bibliographie}{15}{section.7}%
\contentsline {section}{\numberline {3}Partie Électronique}{6}{section.3}%
\contentsline {subsection}{\numberline {3.1}Semaine 1}{6}{subsection.3.1}%
\contentsline {subsubsection}{\numberline {3.1.1}Expérimentaions}{6}{subsubsection.3.1.1}%
\contentsline {paragraph}{Protocole Expérimental}{6}{section*.3}%
\contentsline {paragraph}{Analyse des résultats}{9}{section*.4}%
\contentsline {subsubsection}{\numberline {3.1.2}Bilan et confrontation des résultats}{10}{subsubsection.3.1.2}%
\contentsline {subsection}{\numberline {3.2}Semaines 2 et 3}{10}{subsection.3.2}%
\contentsline {subsubsection}{\numberline {3.2.1}Démarche 1}{10}{subsubsection.3.2.1}%
\contentsline {paragraph}{Temps 1:}{10}{section*.5}%
\contentsline {paragraph}{Caractérisation du signal Vdistance(t):}{10}{section*.6}%
\contentsline {paragraph}{Le 555 Astable}{11}{section*.7}%
\contentsline {paragraph}{Temps 2}{12}{section*.8}%
\contentsline {paragraph}{Temps 3}{12}{section*.9}%
\contentsline {subsubsection}{\numberline {3.2.2}Démarche 2}{12}{subsubsection.3.2.2}%
\contentsline {paragraph}{Activité 1}{12}{section*.10}%
\contentsline {paragraph}{Activité 3}{13}{section*.11}%
\contentsline {paragraph}{Activité 4}{13}{section*.12}%
\contentsline {paragraph}{Activité 5}{13}{section*.13}%
\contentsline {section}{\numberline {4}Partie Mathématiques}{13}{section.4}%
\contentsline {subsection}{\numberline {4.1}Semaine 1}{13}{subsection.4.1}%
\contentsline {subsubsection}{\numberline {4.1.1}Pourquoi les systèmes vus en ZG étaient descriptibles par des équations différentielles ?}{13}{subsubsection.4.1.1}%
\contentsline {section}{\numberline {5}Partie Informatique}{14}{section.5}%
\contentsline {section}{\numberline {6}Synthèse}{16}{section.6}%
\contentsline {subsection}{\numberline {6.1}Similarités théorique (calculées lor de la première activité)}{16}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Similarités lors de l’expérimentation}{16}{subsection.6.2}%
\contentsline {section}{\numberline {7}Bibliographie}{17}{section.7}%
Time(s),y,y',"y"""
0.10999999999999999,0.0065085593054112385,0.10769658889900216,0.957492377902155
0.22000000000000006,0.02454386284372199,0.20998220746236732,0.906165353969472
0.3300000000000001,0.05348048504027871,0.3063627524027224,0.8506072133826909
0.4400000000000002,0.09264244230643467,0.3964074297096378,0.7913955896692187
0.5500000000000003,0.1413101813958493,0.4797490880055963,0.7291091872372344
0.6600000000000004,0.198727576228004,0.556084084881768,0.6643236192969688
0.7700000000000005,0.26410888305057323,0.6251717073070485,0.5976074472797982
0.8800000000000006,0.3366456062706541,0.6868331694655885,0.529518441233098
0.9900000000000007,0.41551322997623175,0.7409502133761559,0.4606000782570838
1.1000000000000008,0.4998777730644544,0.7874633393782883,0.39137829362076476
1.2100000000000009,0.5889021289629202,0.82636969503448,0.3223584967657257
1.320000000000001,0.6817521541448918,0.8577206521957457,0.25402286199592483
1.430000000000001,0.777602472970027,0.881619102912736,0.18682790127546767
1.5400000000000011,0.875641969800155,0.8982165055508947,0.12120232422977362
1.6500000000000012,0.975078942816766,0.9077097128922412,0.057545188183129925
1.7600000000000013,1.0751458974759402,0.9103376141861419,-0.003775661119381435
1.8700000000000014,1.175103961051063,0.9063776230561131,-0.06242485955295807
1.9800000000000015,1.2742469032086587,0.8961420428898509,-0.1181005088592334
2.0899999999999994,1.3719047510139752,0.8799743408469478,-0.17053488042377773
2.199999999999997,1.4674469901479295,0.858245360925862,-0.21949484567625233
2.3099999999999947,1.5602853474144533,0.8313495056521498,-0.2647820418429909
2.4199999999999924,1.6498761528074999,0.7997009148981429,-0.30623278328751835
2.52999999999999,1.7357222824718777,0.7637296691349826,-0.34371773004247963
2.6399999999999877,1.8173746868153475,0.7238780430666579,-0.3771413263629233
2.7499999999999853,1.8944335107962798,0.6805968341181438,-0.406441023213169
2.859999999999983,1.9665488160087696,0.6343417886618603,-0.43158629953617944
2.9699999999999807,2.033420916604228,0.5855701471845293,-0.45257749794502145
3.0799999999999783,2.0948003433156983,0.5347373278361126,-0.4694444911213327
3.189999999999976,2.1504874518808874,0.48229376597977885,-0.48224519570739477
3.2999999999999736,2.2003316939861355,0.4286819254924175,-0.49106395083904986
3.4099999999999713,2.244230570472212,0.3743334956643959,-0.4960097786898586
3.519999999999969,2.2821282879511826,0.3196667856299307,-0.4972145444868499
3.6299999999999666,2.3140141411808473,0.2650843263399491,-0.4948310334201288
3.7399999999999642,2.3399206445299288,0.21097068818140483,-0.4890309617082639
3.849999999999962,2.3599214366453256,0.15769052046375492,-0.48000293880513534
3.9599999999999596,2.3741289830058583,0.1055868171470249,-0.46795039734883803
4.069999999999958,2.3826921014197953,0.05497941138813341,-0.4530895069666685
4.179999999999955,2.3857933357019427,0.006163699743599791,-0.43564708747002423
4.289999999999953,2.3836462027574647,-0.040590404802762964,-0.41585853630741987
4.399999999999951,2.376492338111887,-0.0850392934101709,-0.3939657844011293
4.509999999999948,2.364598564569058,-0.12696625947793036,-0.3702152936818577
4.619999999999946,2.348253908161043,-0.16618187961079864,-0.34485610876503126
4.729999999999944,2.3277665848865725,-0.2025241841081169,-0.3181379742905075
4.839999999999941,2.3034609809290445,-0.235858624842093,-0.2903095284835764
4.949999999999939,2.2756746481127377,-0.2660778494923951,-0.2616165824976293
5.0599999999999365,2.2447553353090863,-0.2931012920947001,-0.23230049407644593
5.169999999999934,2.211058075355852,-0.31687459073778523,-0.20259664303496372
5.279999999999932,2.1749423458134647,-0.33736884400581374,-0.1727330150098274
5.3899999999999295,2.136769320567305,-0.35457971840917923,-0.1429288988826971
5.499999999999927,2.096899227905003,-0.3685264195790199,-0.11339370223781908
5.609999999999925,2.055688829266448,-0.37925054041846307,-0.08432588818774511
5.7199999999999225,2.013489031393601,-0.3868147997097534,-0.05591203589409388
5.82999999999992,1.9706426431095063,-0.39130168487329614,-0.028326026130145676
5.939999999999918,1.927482286442926,-0.39281201266562854,-0.001728352284636303
6.0499999999999154,1.884328470298202,-0.3914634215923305,0.023734443703270047
6.159999999999913,1.841487833360238,-0.38738880970337813,0.047930211854406046
6.269999999999911,1.7992515614323104,-0.3807347312374156,0.07074151330136114
6.379999999999908,1.7578939829396307,-0.371659765293277,0.09206582104595662
6.489999999999906,1.717671344903412,-0.36033286933765696,0.1118156060009936
6.599999999999904,1.6788207703072453,-0.34693172991321913,0.12991831265206955
6.709999999999901,1.6415593964477222,-0.33164112239806837,0.14631622927329868
6.819999999999899,1.6060836925916278,-0.3146512910919983,0.1609662581679424
6.929999999999897,1.572568954059125,-0.29615636027404696,0.17383959188001952
7.039999999999894,1.5411689687218006,-0.27635278619650744,0.18492130173528465
7.149999999999892,1.512015850851186,-0.25543785925959545,0.19420984541924613
7.25999999999989,1.4852200362815549,-0.23360826485536618,0.2017165005864271
7.369999999999887,1.4608704319638488,-0.21105871058608844,0.20746473171948765
7.479999999999885,1.4390347121880918,-0.18798062675788127,0.21148949762023117
7.589999999999883,1.419759753041613,-0.16456094623163217,0.21383650701836865
7.69999999999988,1.4030721960509216,-0.14098096888648626,0.21456142983004278
7.809999999999878,1.3889791314267144,-0.11741531512274682,0.21372907158868837
7.919999999999876,1.3774688908940758,-0.09403097200682509,0.21141251850827691
8.029999999999873,1.3685119397425927,-0.07098643484660096,0.20769226052610956
8.139999999999871,1.3620618574725012,-0.04843094618656632,0.20265529951205474
8.249999999999869,1.3580563962410752,-0.02650383343344797,0.19639424962663987
8.359999999999866,1.3564186062257544,-0.005333945569303,0.1890064365651133
8.469999999999864,1.3570580170140014,0.014960811315365032,0.18059300214191298
8.579999999999862,1.359871864201084,0.03427384062721853,0.17125802035364002
8.68999999999986,1.364746350522071,0.05251012562783883,0.16110763071223788
8.799999999999857,1.3715579310590778,0.06958640577198369,0.15024919426746175
8.909999999999854,1.380174612344669,0.08543126182729267,0.13879047734261585
9.019999999999852,1.3904572555225194,0.09998511310434736,0.12683886759375052
9.12999999999985,1.4022608741219371,0.11320013060750912,0.11450062657377424
9.239999999999847,1.4154359174484534,0.1250400703506043,0.10188018254296183
9.349999999999845,1.4298295310830726,0.13548003146628598,0.08907946681971857
9.459999999999843,1.4452867865125116,0.1445061440731434,0.07619729651372953
9.56999999999984,1.4616518724763754,0.15211519215010869,0.06332880603115654
9.679999999999838,1.4787692412092859,0.15831417690353858,0.05056492929160061
9.789999999999836,1.496484703370997,0.16311982629899427,0.03799193415220692
9.899999999999833,1.5146464660901922,0.16655805656799375,0.025691010098489175
10.009999999999831,1.5331061091926717,0.16866339159097887,0.013737909836898932
10.119999999999829,1.551719495336881,0.16947834610280976,0.0022026450134181585
10.229999999999826,1.5703476104342815,0.16905277866793642,-0.00885076411218455
10.339999999999824,1.588857331384128,0.1674432203308977,-0.019364485583183377
10.449999999999822,1.6071221187972944,0.16471218476608968,-0.02928702015684337
10.55999999999982,1.6250226330175799,0.16092746563113658,-0.038573294447003637
10.669999999999817,1.6424472723674133,0.15616142667317773,-0.04718470434706823
10.779999999999815,1.6592926331443176,0.15049028994958405,-0.055089110569002786
10.889999999999812,1.67546389147145,0.14399342730678227,-0.06226078839532345
10.99999999999981,1.6908751076568687,0.13675266001584332,-0.06868033397626849
11.109999999999808,1.7054494542390877,0.1288515711941982,-0.07433452971281795
11.219999999999805,1.7191193693884455,0.12037483535223846,-0.0792161714476397
11.329999999999803,1.731826637792697,0.11140756909462984,-0.08332386034026329
11.4399999999998,1.7435224015791948,0.10203470668190236,-0.08666176242990586
11.549999999999798,1.7541671042135265,0.09234040382124287,-0.08923933898964409
11.659999999999796,1.7637303706643803,0.08240747270934191,-0.09107105084950695
11.769999999999794,1.7721908274357985,0.07231685099749553,-0.09217603991414891
11.879999999999791,1.7795358663403449,0.06214710699273263,-0.0925777911238389
11.989999999999789,1.785761356119773,0.05197398305122508,-0.09230377810647217
12.099999999999786,1.790871306213581,0.04186997876422946,-0.09138509574423181
12.209999999999784,1.7948774871307025,0.03190397518477643,-0.08985608283255353
12.319999999999782,1.7977990119960712,0.022140900997594703,-0.08775393794246489
12.42999999999978,1.7996618839227518,0.0126414411975211,-0.08511833151152037
12.539999999999777,1.800498513902801,0.0034617885149381997,-0.08199101708490575
12.649999999999775,1.8003472139172776,-0.005346562487535692,-0.07841544450831073
12.759999999999772,1.7992516699393475,-0.013736979023099435,-0.07443637773946499
12.86999999999977,1.7972603994458278,-0.02166781205415787,-0.07009951979734774
12.979999999999768,1.7944261979636533,-0.029102477559263963,-0.06545114720867673
13.089999999999765,1.7908055790604906,-0.03600949827131196,-0.060537756141965327
13.199999999999763,1.7864582120451782,-0.0423625072950227,-0.055405722241835154
13.30999999999976,1.7814463614759972,-0.04814021522215687,-0.050100975992036556
13.419999999999758,1.7758343323851464,-0.05332634255270142,-0.0446686952463089
13.529999999999756,1.769687924918589,-0.057909519399036574,-0.03915301637342661
13.639999999999754,1.763073901863918,-0.061883154597513416,-0.03359676526800248
13.749999999999751,1.7560594722974467,-0.06524527647782583,-0.028041209283337976
13.859999999999749,1.7487117943277313,-0.06799834764507835,-0.022525830948270986
13.969999999999747,1.7410974996484951,-0.07014905621271096,-0.017088124137840444
14.079999999999744,1.7332822423418077,-0.07170808598677031,-0.011763413179013193
14.189999999999742,1.7253302740946175,-0.07268986814387338,-0.006584695188839751
14.29999999999974,1.7173040477105819,-0.0731123169671778,-0.0015825057643383822
14.409999999999737,1.709263850516733,-0.072996552207457,0.0032151920278096213
14.519999999999735,1.7012674689828995,-0.07236661062078317,0.007783095577157617
14.629999999999733,1.6933698855929809,-0.07124914920125315,0.012098627941270257
14.73999999999973,1.685623008732957,-0.06967314257763683,0.01614198085925178
14.849999999999728,1.6780754360927141,-0.06766957697785234,0.019896136218519267
14.959999999999726,1.6707722518189654,-0.06527114308590046,0.023346866751471573
15.069999999999723,1.6637548574062626,-0.06251193002350595,0.026482716852915478
15.17999999999972,1.6570608360737082,-0.05942712258443597,0.029294964512091237
15.289999999999718,1.6507238501476986,-0.05605270373455146,0.03177756544457255
15.399999999999716,1.6447735707569697,-0.052425164266372816,0.033927080589125524
15.509999999999714,1.6392356389463316,-0.04858122136459127,0.03574258820266074
15.619999999999711,1.6341316571305555,-0.04455754769982593,0.03722558184276925
15.729999999999709,1.6294792096406083,-0.04039051252329123,0.03837985557210011
15.839999999999707,1.625291910961341,-0.0361159360861696,0.039211377752154775
15.949999999999704,1.621579480123205,-0.031768858555619714,0.03972815481625602
16.05999999999971,1.618347839590868,-0.027383324445700612,0.039940086422776466
16.169999999999728,1.6155992368888477,-0.022992183427228,0.039858813390581505
16.279999999999745,1.6133323871184713,-0.018626908226821202,0.03949755980952285
16.389999999999763,1.6115426344514896,-0.014317430173224104,0.038870970700157215
16.49999999999978,1.6102221306332951,-0.010091992799400413,0.03799494656926372
16.609999999999797,1.6093600284925489,-0.005977023762867693,0.03688647617172747
16.719999999999814,1.6089426884336937,-0.0019970252051308333,0.03556346874558769
16.82999999999983,1.60895389588377,0.001825517465281176,0.03404458693616197
16.93999999999985,1.6093750876745323,0.005470208512035838,0.0323490815678098
17.049999999999866,1.6101855853643983,0.008918796802040928,0.03049662935879216
17.159999999999883,1.6113628335414643,0.012155213114329173,0.02850717460650176
17.2699999999999,1.6128826411978863,0.015165590321485872,0.026400775797793985
17.379999999999917,1.6147194243264336,0.0179382670387994,0.024197458022944707
17.489999999999934,1.616846447961103,0.020463775428225937,0.021917071992587522
17.59999999999995,1.619236065964312,0.022734813927320113,0.019579160375550964
17.70999999999997,1.6218599569524386,0.024746205747283565,0.017202832092477083
17.819999999999986,1.6246893548482986,0.026494844049088508,0.014806645116144601
17.930000000000003,1.627695272652557,0.027979624762178513,0.012408498245148003
18.04000000000002,1.6308487181350286,0.029201368056538085,0.010025532233641332
18.150000000000038,1.6341209002603085,0.030162729516027338,0.007674040576807428
18.260000000000055,1.6374834252792223,0.030868102088928352,0.005369390170109289
18.370000000000072,1.6409084815371597,0.03132350991083903,0.0031259519807566027
18.48000000000009,1.6443690121715315,0.031536495105622044,0.0009570417926366703
18.590000000000106,1.6478388749924344,0.031515998672368914,-0.0011251289883271731
18.700000000000124,1.6512929889622041,0.03127223656061411,-0.003109492552414106
18.81000000000014,1.6547074668100545,0.030816572022716114,-0.004986154079300142
18.920000000000158,1.6580597334366152,0.030161385311835327,-0.006746411520915818
19.030000000000175,1.6613286298791297,0.02931994176673494,-0.008382766047762336
19.140000000000192,1.6644945027206681,0.0283062592911961,-0.00988892348708037
19.25000000000021,1.6675392789352579,0.027134976196677433,-0.011259787131170262
19.360000000000227,1.6704465262647707,0.025821220332488317,-0.012491442339219838
19.470000000000244,1.673201499322169,0.024380480378723972,-0.013581133396103118
19.58000000000026,1.6757911717088532,0.02282848012407831,-0.014527233126705452
19.69000000000028,1.6782042545208888,0.0211810564939631,-0.015329205794331946
19.800000000000296,1.6804312016995564,0.01945404203467571,-0.015987563836743046
19.910000000000313,1.6824642027555756,0.01766315249722594,-0.016503819013305554
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