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MarcoB
MarcoB
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I am using TransformedFieldTransformedField to convert a system of ODEs from Cartesian to polar coordinates:

TransformedField["Cartesian"TransformedField[
  "Cartesian" -> "Polar",
  {\[Mu]μ x1 - x2 -  \[Sigma]σ x1 (x1^2 + x2^2), x1 + \[Mu]μ x2 - \[Sigma]σ x2 
 (x1^2 + x2^2)}, 
  {x1, x2} -> {r, \[Theta]θ} 
] // Simplify

and I get the result

{r \[Mu]μ - r^3 \[Sigma]σ, r}

but I am pretty sure that the right answer should be

{r \[Mu]μ - r^3 \[Sigma]σ, 1}

Where is the error?

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates:

TransformedField["Cartesian" -> "Polar",
{\[Mu] x1 - x2 -  \[Sigma] x1 (x1^2 + x2^2),x1 + \[Mu] x2 - \[Sigma] x2 
 (x1^2 + x2^2)}, 
{x1,x2} -> {r, \[Theta]}] // Simplify

and I get the result

{r \[Mu] - r^3 \[Sigma], r}

but I am pretty sure that the right answer should be

{r \[Mu] - r^3 \[Sigma], 1}

Where is the error?

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates:

TransformedField[
  "Cartesian" -> "Polar",
  {μ x1 - x2 -  σ x1 (x1^2 + x2^2), x1 + μ x2 - σ x2 (x1^2 + x2^2)}, 
  {x1, x2} -> {r, θ} 
] // Simplify

and I get the result

{r μ - r^3 σ, r}

but I am pretty sure that the right answer should be

{r μ - r^3 σ, 1}

Where is the error?

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rpa
rpa
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Error in TransformedField

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates:

TransformedField["Cartesian" -> "Polar",
{\[Mu] x1 - x2 -  \[Sigma] x1 (x1^2 + x2^2),x1 + \[Mu] x2 - \[Sigma] x2 
(x1^2 + x2^2)}, 
{x1,x2} -> {r, \[Theta]}] // Simplify

and I get the result

{r \[Mu] - r^3 \[Sigma], r}

but I am pretty sure that the right answer should be

{r \[Mu] - r^3 \[Sigma], 1}

Where is the error?