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1. PRODUCTOS ENTRE CAMPOS VECTORIALES
a = {x, 2 * y, 3 * z};
b = {x ^ 3, y ^ 2, z};
c = {y * z, x * z, x * y};
AxB + BxC
cruz1 = Cross[a, b]
2 y z - 3 y 2 z, - x z + 3 x 3 z, - 2 x 3 y + x y 2
cruz2 = Cross[b, c]
x y 3 - x z 2 , - x 4 y + y z 2 , x 4 z - y 3 z
cruz1 + cruz
x y 3 + 2 y z - 3 y 2 z - x z 2 , - x 4 y - x z + 3 x 3 z + y z 2 , - 2 x 3 y + x y 2 + x 4 z - y 3 z
A·C
pp = Dot[a, c]
6 x y z
(A + B) x C)·C
d = a + b
x + x 3 , 2 y + y 2 , 4 z
cruz3 = Cross[d, c]
2 x y 2 + x y 3 - 4 x z 2 , - x 2 y - x 4 y + 4 y z 2 , x 2 z + x 4 z - 2 y 2 z - y 3 z
pp1 = Dot[cruz3, c]
x y x 2 z + x 4 z - 2 y 2 z - y 3 z + y z 2 x y 2 + x y 3 - 4 x z 2 + x z - x 2 y - x 4 y + 4 y z 2
2. GRAFICOS
v = x ^ 2 / 9 + (y - 2 ) ^ 2 / 16
x 2 9
(- 2 + y) 2
campoelectrico = - Grad[v, {x, y}, "Cartesian"]
-
2 x 9
2 - y 8
gr1 = ContourPlot[v, {x, - 20, 20}, {y, - 20, 20}]
0
10
20
gr2 = StreamPlot[campoelectrico, {x, - 20, 20}, {y, - 20, 20}]
0
10
20
In[7]:= G2^ =^ Grad[c1,^ {r,^ θ,^ ϕ}, "Spherical"]
Out[7]= 4 r 3 Cos[θ] 2 Cos[ϕ] Sin[θ] 2 Sin[ϕ],
r 2 r 4 Cos[θ] 3 Cos[ϕ] Sin[θ] Sin[ϕ] - 2 r 4 Cos[θ] Cos[ϕ] Sin[θ] 3 Sin[ϕ], 1 r
Csc[θ] r 4 Cos[θ] 2 Cos[ϕ] 2 Sin[θ] 2 - r 4 Cos[θ] 2 Sin[θ] 2 Sin[ϕ] 2
TRANSFORME AHORA EL CAMPO U A COORDENADAS
ESFERICAS Y ENCUENTRE SU GRADIENTE EN ESTAS COORDENADAS
In[8]:= c2 = FullSimplify[ TransformedField["Cartesian" → "Spherical", u[x, y, z], {x, y, z} → {r, θ, ϕ}]]
Out[8]= r 4 Cos[θ] 2 Cos[ϕ] Sin[θ] 2 Sin[ϕ]
In[9]:= G2 = Grad[c2, {r, θ, ϕ}, "Spherical"]
Out[9]= 4 r^3 Cos[θ]^2 Cos[ϕ]^ Sin[θ]^2 Sin[ϕ],
r 2 r 4 Cos[θ] 3 Cos[ϕ] Sin[θ] Sin[ϕ] - 2 r 4 Cos[θ] Cos[ϕ] Sin[θ] 3 Sin[ϕ], 1 r
Csc[θ] r 4 Cos[θ] 2 Cos[ϕ] 2 Sin[θ] 2 - r 4 Cos[θ] 2 Sin[θ] 2 Sin[ϕ] 2
ENCUENTRE LA DIVERGENCIA, ROTACIONAL,
Y LAPLACIANO DEL CAMPO VECTORIAL F EN COORDENADAS CARTESIANAS
d1 = Div[F[x, y, z], {x, y, z}, "Cartesian"] 0
rot1 = Curl[F[x, y, z], {x, y, z}, "Cartesian"] {- 1 + x, - y, 1 - 2 y}
l1 = Laplacian[F[x, y, z], {x, y, z}, "Cartesian"] {2, 0, 0}
TRANSFORME ESTE CAMPO EN COORDENADAS CILINDRICAS Y
VUELVA A ENCONTRAR SU DIVERGENCIA, ROTACIONAL Y LAPLACIANO
c3 = FullSimplify[ TransformedField["Cartesian" → "Cylindrical", F[x, y, z], {x, y, z} → {ρ, ϕ, Z}]] Sin[ϕ] (Z + ρ Cos[ϕ] ( 1 + ρ Sin[ϕ])), Cos[ϕ] (Z + ρ Cos[ϕ]) - ρ 2 Sin[ϕ] 3 , ρ 2 Cos[ϕ] Sin[ϕ]
d2 = Div[c3, {ρ, ϕ, Z}, "Cylindrical"] Sin[ϕ] (ρ Cos[ϕ] Sin[ϕ] + Cos[ϕ] ( 1 + ρ Sin[ϕ])) + 1 ρ
- ρ Cos[ϕ] Sin[ϕ] - (Z + ρ Cos[ϕ]) Sin[ϕ] -
3 ρ 2 Cos[ϕ] Sin[ϕ] 2 + Sin[ϕ] (Z + ρ Cos[ϕ] ( 1 + ρ Sin[ϕ]))
rot2 = Curl[c3, {ρ, ϕ, Z}, "Cylindrical"]
- Cos[ϕ] +
ρ 2 Cos[ϕ] 2 - ρ 2 Sin[ϕ] 2 ρ
, Sin[ϕ] - 2 ρ Cos[ϕ] Sin[ϕ],
Cos[ϕ] 2 - 2 ρ Sin[ϕ] 3 -
ρ
- Cos[ϕ] (Z + ρ Cos[ϕ]) + ρ 2 Sin[ϕ] 3 +
Cos[ϕ] (Z + ρ Cos[ϕ] ( 1 + ρ Sin[ϕ])) + Sin[ϕ] ρ 2 Cos[ϕ] 2 - ρ Sin[ϕ] ( 1 + ρ Sin[ϕ])
l2 = Laplacian[c3, {ρ, ϕ, Z}, "Cylindrical"]
2 Cos[ϕ] Sin[ϕ] 2 +
1 ρ
Sin[ϕ] (ρ Cos[ϕ] Sin[ϕ] + Cos[ϕ] ( 1 + ρ Sin[ϕ])) -
ρ
- ρ Cos[ϕ] Sin[ϕ] -
(Z + ρ Cos[ϕ]) Sin[ϕ] - 3 ρ 2 Cos[ϕ] Sin[ϕ] 2 + Sin[ϕ] (Z + ρ Cos[ϕ] ( 1 + ρ Sin[ϕ])) + 1 ρ
ρ Cos[ϕ] Sin[ϕ] + (Z + ρ Cos[ϕ]) Sin[ϕ] + 3 ρ 2 Cos[ϕ] Sin[ϕ] 2 +
Sin[ϕ] - 3 ρ 2 Cos[ϕ] Sin[ϕ] - ρ Cos[ϕ] ( 1 + ρ Sin[ϕ]) - Sin[ϕ]
(Z + ρ Cos[ϕ] ( 1 + ρ Sin[ϕ])) + 2 Cos[ϕ] ρ 2 Cos[ϕ] 2 - ρ Sin[ϕ] ( 1 + ρ Sin[ϕ]) ,
ρ
Cos[ϕ] 2 - 2 ρ Sin[ϕ] 3 +
ρ
- Cos[ϕ] (Z + ρ Cos[ϕ]) + ρ 2 Sin[ϕ] 3 + Cos[ϕ]
(Z + ρ Cos[ϕ] ( 1 + ρ Sin[ϕ])) + Sin[ϕ] ρ 2 Cos[ϕ] 2 - ρ Sin[ϕ] ( 1 + ρ Sin[ϕ]) + 1 ρ
- ρ Cos[ϕ] 2 - Cos[ϕ] (Z + ρ Cos[ϕ]) - 6 ρ 2 Cos[ϕ] 2 Sin[ϕ] + 2 ρ Sin[ϕ] 2 +
3 ρ 2 Sin[ϕ] 3 + Cos[ϕ] (Z + ρ Cos[ϕ] ( 1 + ρ Sin[ϕ])) +
Sin[ϕ] ρ 2 Cos[ϕ] 2 - ρ Sin[ϕ] ( 1 + ρ Sin[ϕ]) , 0
4. OTRAS COSAS
AJUSTE NO LINEAL
vector = {4, 4.8, 5.1, 6, 7.2, 8.3, 9, 10, 10.9, 12.2}
{4, 4.8, 5.1, 6, 7.2, 8.3, 9, 10, 10.9, 12.2}
Dat = Table[{i, vector[[i]]}, {i, 1, Length[vector], 1}]
{{1, 4}, {2, 4.8}, {3, 5.1}, {4, 6}, {5, 7.2}, {6, 8.3}, {7, 9}, {8, 10}, {9, 10.9}, {10, 12.2}}
gra2 = Plot[Normal[ajuste], {x, 0, 11}]
2 4 6 8 10
6
8
10
12
14
Show[gra1, gra2]
2 4 6 8 10
2
4
6
8
10
12
GRAFICO DE DISCREPANCIAS
Needs["ErrorBarPlots`"]
g = ErrorListPlot[{{9.77, 0.03}, {9.82, 0.04}}, PlotRange → {{0, 3}, {9.7, 9.9}}, PlotLegends → {"Mediciones"}]
0.5 1.0 1.5 2.0 2.5 3.
Mediciones
ref = Plot[9.8, {x, 0, 4}, PlotStyle → {Red, Dashed}, PlotLegends → {"Teorico"}]
1 2 3 4
5
10
15
20
Teorico
Show[g, ref, Ticks → {{{1, "Medida 1"}, {2, "Medida 2"}}, Automatic}, AxesLabel → {None, "m/s^2"}, PlotLabel → "Grafico de Discrepancia"]
Medida 1 Medida 2
m/s^
Grafico de Discrepancia
Mediciones
Teorico
NonlinearModelFit::ivar : x^3 is not a valid variable.
NonlinearModelFit::ivar : x^3 is not a valid variable.
