MANU1 _U1_A2_KAAM.docx

8/11/2019 MANU1 _U1_A2_KAAM.docx

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Anlisis numrico I

Unidad 1.Fundamentos

Actividad 2. Modelacin matemtica.

Karla Judith Andrew Mndez.

AL12509552.

Como describimos en la seccin de Modelacin Matemtica el hacer un modelo implica

observar un fenmeno y traducirlo a lenguaje matemtico. Esta traduccin no es sencilla

de automatizar, es decir, puede ser muy personal y variar de persona a persona pero en

esa seccin leste un bosquejo de como hacerlo. A continuacin implementaremos en

Octave como se modela el tiro parablico.

La ecuacin que describe el tiro parablico desde el origen es:

()

donde

y es la velocidad inicial del cuerpo proyectado.

La tarea es crear una funcin en Octave que recibe dos parmetros y regresa un escalar

que representar la altura del proyectil en cada tiempo . Debers mostrar la trayectoria

()seguida para las siguientes valores de y vectores

V Vectores de T

10 (0,10,100)

25 (0,20,250)

100 (0,50,300)

Primero en el editor creamos la funcin parabolico.

Ya en octave llamamos la funcin con valor v de 10.

>>> y=parabolico(10)y =


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Columns 1 through 6:0.00000 0.96011 1.82022 2.58035 3.24049 3.80063Columns 7 through 12:4.26079 4.62096 4.88113 5.04132 5.10152 5.06173Columns 13 through 18:4.92195 4.68218 4.34241 3.90266 3.36292 2.72319Columns 19 through 24:1.98347 1.14376 0.20406 -0.83563 -1.97531 -3.21498Columns 25 through 30:-4.55464 -5.99429 -7.53393 -9.17355 -10.91317 -12.75278Columns 31 through 36:-14.69238 -16.73197 -18.87154 -21.11111 -23.45067 -25.89022Columns 37 through 42:-28.42975 -31.06928 -33.80880 -36.64830 -39.58780 -42.62728Columns 43 through 48:-45.76676 -49.00622 -52.34568 -55.78512 -59.32456 -62.96398Columns 49 through 54:-66.70340 -70.54280 -74.48220 -78.52158 -82.66095 -86.90032Columns 55 through 60:-91.23967 -95.67901 -100.21835 -104.85767 -109.59698 -114.43628Columns 61 through 66:-119.37557 -124.41486 -129.55413 -134.79339 -140.13264 -145.57188Columns 67 through 72:-151.11111 -156.75033 -162.48954 -168.32874 -174.26793 -180.30711Columns 73 through 78:-186.44628 -192.68544 -199.02459 -205.46373 -212.00286 -218.64198Columns 79 through 84:-225.38108 -232.22018 -239.15927 -246.19835 -253.33741 -260.57647Columns 85 through 90:-267.91552 -275.35456 -282.89358 -290.53260 -298.27160 -306.11060Columns 91 through 96:-314.04959 -322.08856 -330.22753 -338.46648 -346.80543 -355.24436Columns 97 through 100:-363.78329 -372.42220 -381.16111 -390.00000>>>

Creamos de nuevo una funcin llamada parabolico1

Ahora llamamos la funcin con valor de v=25


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>>> y=parabolico1(25)y =Columns 1 through 6:0.0000e+000 1.9764e+000 3.8896e+000 5.7396e+000 7.5263e+000 9.2499e+000Columns 7 through 12:1.0910e+001 1.2507e+001 1.4041e+001 1.5512e+001 1.6919e+001 1.8263e+001Columns 13 through 18:1.9544e+001 2.0762e+001 2.1916e+001 2.3008e+001 2.4036e+001 2.5001e+001Columns 19 through 24:2.5902e+001 2.6741e+001 2.7516e+001 2.8228e+001 2.8876e+001 2.9462e+001Columns 25 through 30:2.9984e+001 3.0443e+001 3.0839e+001 3.1171e+001 3.1441e+001 3.1647e+001Columns 31 through 36:3.1790e+001 3.1869e+001 3.1886e+001 3.1839e+001 3.1729e+001 3.1556e+001Columns 37 through 42:3.1319e+001 3.1020e+001 3.0657e+001 3.0231e+001 2.9741e+001 2.9189e+001Columns 43 through 48:2.8573e+001 2.7894e+001 2.7152e+001 2.6346e+001 2.5478e+001 2.4546e+001Columns 49 through 54:2.3551e+001 2.2492e+001 2.1371e+001 2.0186e+001 1.8938e+001 1.7626e+001Columns 55 through 60:1.6252e+001 1.4814e+001 1.3313e+001 1.1749e+001 1.0122e+001 8.4312e+000Columns 61 through 66:6.6773e+000 4.8602e+000 2.9800e+000 1.0364e+000 -9.7031e-001 -3.0403e+000Columns 67 through 72:-5.1735e+000 -7.3699e+000 -9.6295e+000 -1.1952e+001 -1.4338e+001 -1.6788e+001Columns 73 through 78:-1.9300e+001 -2.1876e+001 -2.4515e+001 -2.7217e+001 -2.9983e+001 -3.2811e+001Columns 79 through 84:-3.5703e+001 -3.8658e+001 -4.1677e+001 -4.4758e+001 -4.7903e+001 -5.1111e+001Columns 85 through 90:-5.4382e+001 -5.7717e+001 -6.1114e+001 -6.4575e+001 -6.8100e+001 -7.1687e+001Columns 91 through 96:-7.5337e+001 -7.9051e+001 -8.2828e+001 -8.6669e+001 -9.0572e+001 -9.4539e+001

Columns 97 through 102:-9.8569e+001 -1.0266e+002 -1.0682e+002 -1.1104e+002 -1.1532e+002 -1.1967e+002Columns 103 through 108:-1.2408e+002 -1.2855e+002 -1.3308e+002 -1.3768e+002 -1.4235e+002 -1.4707e+002Columns 109 through 114:-1.5186e+002 -1.5671e+002 -1.6163e+002 -1.6660e+002 -1.7165e+002 -1.7675e+002Columns 115 through 120:-1.8192e+002 -1.8715e+002 -1.9244e+002 -1.9780e+002 -2.0322e+002 -2.0871e+002Columns 121 through 126:-2.1425e+002 -2.1987e+002 -2.2554e+002 -2.3128e+002 -2.3708e+002 -2.4294e+002Columns 127 through 132:-2.4887e+002 -2.5486e+002 -2.6091e+002 -2.6703e+002 -2.7321e+002 -2.7945e+002Columns 133 through 138:-2.8575e+002 -2.9212e+002 -2.9856e+002 -3.0505e+002 -3.1161e+002 -3.1823e+002Columns 139 through 144:-3.2492e+002 -3.3167e+002 -3.3848e+002 -3.4535e+002 -3.5229e+002 -3.5929e+002Columns 145 through 150:-3.6636e+002 -3.7349e+002 -3.8068e+002 -3.8793e+002 -3.9525e+002 -4.0263e+002Columns 151 through 156:-4.1007e+002 -4.1758e+002 -4.2515e+002 -4.3279e+002 -4.4048e+002 -4.4824


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e+002Columns 157 through 162:-4.5607e+002 -4.6395e+002 -4.7190e+002 -4.7992e+002 -4.8799e+002 -4.9613e+002Columns 163 through 168:-5.0433e+002 -5.1260e+002 -5.2093e+002 -5.2932e+002 -5.3778e+002 -5.4630e+002Columns 169 through 174:-5.5488e+002 -5.6352e+002 -5.7223e+002 -5.8100e+002 -5.8984e+002 -5.9874e+002Columns 175 through 180:-6.0770e+002 -6.1672e+002 -6.2581e+002 -6.3496e+002 -6.4418e+002 -6.5345e+002Columns 181 through 186:-6.6280e+002 -6.7220e+002 -6.8167e+002 -6.9120e+002 -7.0079e+002 -7.1045e+002Columns 187 through 192:-7.2017e+002 -7.2995e+002 -7.3980e+002 -7.4971e+002 -7.5968e+002 -7.6972e+002Columns 193 through 198:-7.7982e+002 -7.8998e+002 -8.0021e+002 -8.1049e+002 -8.2085e+002 -8.3126e+002Columns 199 through 204:-8.4174e+002 -8.5228e+002 -8.6289e+002 -8.7356e+002 -8.8429e+002 -8.9508e+002Columns 205 through 210:-9.0594e+002 -9.1686e+002 -9.2785e+002 -9.3890e+002 -9.5001e+002 -9.6118e+002Columns 211 through 216:-9.7242e+002 -9.8372e+002 -9.9508e+002 -1.0065e+003 -1.0180e+003 -1.0296e+003Columns 217 through 222:-1.0412e+003 -1.0529e+003 -1.0646e+003 -1.0764e+003 -1.0883e+003 -1.1002e+003Columns 223 through 228:-1.1122e+003 -1.1243e+003 -1.1364e+003 -1.1486e+003 -1.1608e+003 -1.1731e+003Columns 229 through 234:-1.1855e+003 -1.1979e+003 -1.2104e+003 -1.2230e+003 -1.2356e+003 -1.2483e+003

Columns 235 through 240:-1.2611e+003 -1.2739e+003 -1.2868e+003 -1.2997e+003 -1.3127e+003 -1.3258e+003Columns 241 through 246:-1.3389e+003 -1.3521e+003 -1.3654e+003 -1.3787e+003 -1.3921e+003 -1.4056e+003Columns 247 through 250:-1.4191e+003 -1.4327e+003 -1.4463e+003 -1.4600e+003

Volvemos a crear la funcin en el editor llamada parabolico2


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De nuevo en octavo llamamos la funcin con v=100

>>> y=parabolico2(100)y =Columns 1 through 6:0.0000e+000 1.6585e+001 3.2897e+001 4.8934e+001 6.4697e+001 8.0186e+001Columns 7 through 12:9.5402e+001 1.1034e+002 1.2501e+002 1.3940e+002 1.5352e+002 1.6737e+002Columns 13 through 18:1.8094e+002 1.9423e+002 2.0726e+002 2.2001e+002 2.3248e+002 2.4468e+002Columns 19 through 24:2.5661e+002 2.6826e+002 2.7964e+002 2.9074e+002 3.0157e+002 3.1213e+002Columns 25 through 30:3.2241e+002 3.3242e+002 3.4216e+002 3.5162e+002 3.6080e+002 3.6971e+002Columns 31 through 36:3.7835e+002 3.8672e+002 3.9481e+002 4.0262e+002 4.1016e+002 4.1743e+002Columns 37 through 42:4.2442e+002 4.3114e+002 4.3759e+002 4.4376e+002 4.4966e+002 4.5528e+002Columns 43 through 48:4.6063e+002 4.6571e+002 4.7051e+002 4.7504e+002 4.7929e+002 4.8327e+002Columns 49 through 54:4.8697e+002 4.9041e+002 4.9356e+002 4.9645e+002 4.9905e+002 5.0139e+002Columns 55 through 60:5.0345e+002 5.0524e+002 5.0675e+002 5.0799e+002 5.0895e+002 5.0964e+002Columns 61 through 66:

5.1006e+002 5.1020e+002 5.1007e+002 5.0967e+002 5.0899e+002 5.0803e+002Columns 67 through 72:5.0681e+002 5.0530e+002 5.0353e+002 5.0148e+002 4.9916e+002 4.9656e+002Columns 73 through 78:4.9369e+002 4.9054e+002 4.8712e+002 4.8343e+002 4.7946e+002 4.7522e+002Columns 79 through 84:4.7070e+002 4.6591e+002 4.6084e+002 4.5551e+002 4.4989e+002 4.4401e+002Columns 85 through 90:4.3785e+002 4.3141e+002 4.2470e+002 4.1772e+002 4.1047e+002 4.0293e+002Columns 91 through 96:3.9513e+002 3.8705e+002 3.7870e+002 3.7007e+002 3.6117e+002 3.5200e+002Columns 97 through 102:


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3.4255e+002 3.3282e+002 3.2283e+002 3.1256e+002 3.0201e+002 2.9119e+002Columns 103 through 108:2.8010e+002 2.6873e+002 2.5709e+002 2.4517e+002 2.3298e+002 2.2052e+002Columns 109 through 114:2.0778e+002 1.9477e+002 1.8149e+002 1.6793e+002 1.5409e+002 1.3998e+002Columns 115 through 120:1.2560e+002 1.1095e+002 9.6017e+001 8.0813e+001 6.5335e+001 4.9583e+001Columns 121 through 126:3.3557e+001 1.7257e+001 6.8232e-001 -1.6166e+001 -3.3288e+001 -5.0685e+001Columns 127 through 132:-6.8355e+001 -8.6299e+001 -1.0452e+002 -1.2301e+002 -1.4178e+002 -1.6082e+002Columns 133 through 138:-1.8013e+002 -1.9972e+002 -2.1958e+002 -2.3972e+002 -2.6013e+002 -2.8082e+002Columns 139 through 144:-3.0178e+002 -3.2301e+002 -3.4452e+002 -3.6630e+002 -3.8835e+002 -4.1068e+002Columns 145 through 150:-4.3328e+002 -4.5616e+002 -4.7931e+002 -5.0274e+002 -5.2644e+002 -5.5041e+002Columns 151 through 156:-5.7466e+002 -5.9918e+002 -6.2398e+002 -6.4904e+002 -6.7439e+002 -7.0001e+002Columns 157 through 162:-7.2590e+002 -7.5206e+002 -7.7850e+002 -8.0522e+002 -8.3221e+002 -8.5947e+002Columns 163 through 168:-8.8700e+002 -9.1481e+002 -9.4290e+002 -9.7126e+002 -9.9989e+002 -1.0288e+003Columns 169 through 174:-1.0580e+003 -1.0874e+003 -1.1172e+003 -1.1472e+003 -1.1774e+003 -1.2080e+003Columns 175 through 180:-1.2388e+003 -1.2699e+003 -1.3013e+003 -1.3329e+003 -1.3649e+003 -1.3970e+003Columns 181 through 186:-1.4295e+003 -1.4623e+003 -1.4953e+003 -1.5286e+003 -1.5621e+003 -1.5960e+003

Columns 187 through 192:-1.6301e+003 -1.6645e+003 -1.6991e+003 -1.7341e+003 -1.7693e+003 -1.8048e+003Columns 193 through 198:-1.8405e+003 -1.8765e+003 -1.9129e+003 -1.9494e+003 -1.9863e+003 -2.0234e+003Columns 199 through 204:-2.0608e+003 -2.0985e+003 -2.1364e+003 -2.1747e+003 -2.2132e+003 -2.2519e+003Columns 205 through 210:-2.2910e+003 -2.3303e+003 -2.3699e+003 -2.4098e+003 -2.4499e+003 -2.4903e+003Columns 211 through 216:-2.5310e+003 -2.5720e+003 -2.6132e+003 -2.6547e+003 -2.6965e+003 -2.7386e+003Columns 217 through 222:-2.7809e+003 -2.8235e+003 -2.8664e+003 -2.9096e+003 -2.9530e+003 -2.9967e+003Columns 223 through 228:-3.0407e+003 -3.0849e+003 -3.1295e+003 -3.1743e+003 -3.2193e+003 -3.2647e+003Columns 229 through 234:-3.3103e+003 -3.3562e+003 -3.4024e+003 -3.4488e+003 -3.4955e+003 -3.5425e+003Columns 235 through 240:-3.5898e+003 -3.6373e+003 -3.6851e+003 -3.7332e+003 -3.7816e+003 -3.8302e+003Columns 241 through 246:-3.8792e+003 -3.9283e+003 -3.9778e+003 -4.0275e+003 -4.0775e+003 -4.1278


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e+003Columns 247 through 252:-4.1784e+003 -4.2292e+003 -4.2803e+003 -4.3317e+003 -4.3833e+003 -4.4353e+003Columns 253 through 258:-4.4875e+003 -4.5399e+003 -4.5927e+003 -4.6457e+003 -4.6990e+003 -4.7526e+003Columns 259 through 264:-4.8064e+003 -4.8605e+003 -4.9149e+003 -4.9696e+003 -5.0245e+003 -5.0798e+003Columns 265 through 270:-5.1352e+003 -5.1910e+003 -5.2470e+003 -5.3034e+003 -5.3599e+003 -5.4168e+003Columns 271 through 276:-5.4739e+003 -5.5313e+003 -5.5890e+003 -5.6470e+003 -5.7052e+003 -5.7637e+003Columns 277 through 282:-5.8225e+003 -5.8815e+003 -5.9409e+003 -6.0005e+003 -6.0603e+003 -6.1205e+003Columns 283 through 288:-6.1809e+003 -6.2416e+003 -6.3026e+003 -6.3638e+003 -6.4253e+003 -6.4871e+003Columns 289 through 294:-6.5492e+003 -6.6115e+003 -6.6741e+003 -6.7370e+003 -6.8002e+003 -6.8636e+003Columns 295 through 300:-6.9273e+003 -6.9913e+003 -7.0556e+003 -7.1201e+003 -7.1849e+003 -7.2500e+003>>>

MANU1 _U1_A2_KAAM.docx

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