Cartesianas a Cilíndricas

[pic 1]

Cartesianas a Cilíndricas

        VΦ = arctan (Vy/Vx)

        Vp = Vx cosΦ + Vy senΦ

        Vz = Vz

• Vp = 5
• VΦ = 53°
• Vz = 5

[pic 2]

        r = (x^2+y^2+z^2)^(1/2)

        ∇(1/r) = d(1/r)/dx i + d(1/r)/dy j + d(1/r)/dz k

        d(1/r)/dx = d(1/(x^2+y^2+z^2))^(1/2)/dx

        d(1/r)/dx = -x/( x^2+y^2+z^2 )^(3/2)

        Análogamente:

        d(1/r)/dy = -y/( x^2+y^2+z^2 )^(3/2)

        d(1/r)/dz = -z/( x^2+y^2+z^2 )^(3/2)

        ∇(1/r) = - (x i+ y j + z k) /r^3

        En coordenadas esféricas:

        [pic 3][pic 4]

        ∇(1/r) = -1/r^2 er

[pic 5]

[pic 6][pic 7][pic 8][pic 9]

[pic 10]

[pic 11][pic 12]

[pic 13]

[pic 14]

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