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edit approved Jan 21, 2016 at 17:47
VividD
edit approved Jan 21, 2016 at 17:47
VividD
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Now I can use the DivDiv operator to express a differential equation, in this case the continuity equation in hydrodynamics.:

 ({0, 0, 0},1) ({0, 0, 1},0) {nx [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1) ({0, 0, 1},0) ny [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1) ({0, 0, 1},0) nz [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t]} == 0

({0, 0, 0},1) ({0, 0, 1},0) {nx [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1)
({0, 0, 1},0) ny [{x, y, z}, t] + vz[{x, y, z}, t] nz
[{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1)
({0, 0, 1},0) nz [{x, y, z}, t] + vz[{x, y, z}, t] nz
[{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t]} == 0

Now I can use the Div operator to express a differential equation, in this case the continuity equation in hydrodynamics.

 ({0, 0, 0},1) ({0, 0, 1},0) {nx [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1) ({0, 0, 1},0) ny [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1) ({0, 0, 1},0) nz [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t]} == 0

Now I can use the Div operator to express a differential equation, in this case the continuity equation in hydrodynamics:

({0, 0, 0},1) ({0, 0, 1},0) {nx [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1)
({0, 0, 1},0) ny [{x, y, z}, t] + vz[{x, y, z}, t] nz
[{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1)
({0, 0, 1},0) nz [{x, y, z}, t] + vz[{x, y, z}, t] nz
[{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t]} == 0

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m_goldberg
m_goldberg
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I am trying to rearrange and manipulate some vector differential equations in MathematicaMathematica. As far as I understand you have to tell MathematicaMathematica that a variable is a vector by specifying the components of the vector. For example

I would like MathematicaMathematica to write the equation in vectorial form so that I can rearrange it and use vector identities to manipulate it.

Is there a way to do this?

Thanks

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components of the vector. For example

I would like Mathematica to write the equation in vectorial form so that I can rearrange it and use vector identities to manipulate it.

Is there a way to do this?

Thanks

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components of the vector. For example

I would like Mathematica to write the equation in vectorial form so that I can rearrange it and use vector identities to manipulate it.

Is there a way to do this?

Source Link
Holger Schmitz
Holger Schmitz
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Is it possible to do vector calculus in Mathematica?

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components of the vector. For example

r = {x, y, z};

If I want to define vector fields I have to do it in the following way

v = {vx[r, t], vy[r, t], vz[r, t]}; n = {nx[r, t], ny[r, t], nz[r, t]};

Now I can use the Div operator to express a differential equation, in this case the continuity equation in hydrodynamics.

D[n, t] + Div[n*v, r] == 0

My problem is the output I get from this. It looks absolutely horrible and I can't do anything with it.

 ({0, 0, 0},1) ({0, 0, 1},0) {nx [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1) ({0, 0, 1},0) ny [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t], ({0, 0, 0},1) ({0, 0, 1},0) nz [{x, y, z}, t] + vz[{x, y, z}, t] nz [{x, y, z}, t] + ({0, 0, 1},0) ({0, 1, 0},0) nz[{x, y, z}, t] vz [{x, y, z}, t] + vy[{x, y, z}, t] ny [{x, y, z}, t] + ({0, 1, 0},0) ({1, 0, 0},0) ny[{x, y, z}, t] vy [{x, y, z}, t] + vx[{x, y, z}, t] nx [{x, y, z}, t] + ({1, 0, 0},0) nx[{x, y, z}, t] vx [{x, y, z}, t]} == 0

I would like Mathematica to write the equation in vectorial form so that I can rearrange it and use vector identities to manipulate it.

Is there a way to do this?

Thanks