Converting vector in cartesian to cylindrical coordinates












2














This seems like a trivial question, and I'm just not sure if I'm doing it right.

I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.

Relevant equations:
$$A_rho=A_xcosphi+A_ysinphi$$
$$A_phi=−A_xsinphi+A_ycosphi$$
$$A_z=A_z$$

What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?










share|cite|improve this question





























    2














    This seems like a trivial question, and I'm just not sure if I'm doing it right.

    I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.

    Relevant equations:
    $$A_rho=A_xcosphi+A_ysinphi$$
    $$A_phi=−A_xsinphi+A_ycosphi$$
    $$A_z=A_z$$

    What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
    Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?










    share|cite|improve this question



























      2












      2








      2







      This seems like a trivial question, and I'm just not sure if I'm doing it right.

      I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.

      Relevant equations:
      $$A_rho=A_xcosphi+A_ysinphi$$
      $$A_phi=−A_xsinphi+A_ycosphi$$
      $$A_z=A_z$$

      What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
      Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?










      share|cite|improve this question















      This seems like a trivial question, and I'm just not sure if I'm doing it right.

      I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.

      Relevant equations:
      $$A_rho=A_xcosphi+A_ysinphi$$
      $$A_phi=−A_xsinphi+A_ycosphi$$
      $$A_z=A_z$$

      What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
      Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?







      vectors coordinate-systems






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Mar 17 '17 at 0:08









      Community

      1




      1










      asked Jun 13 '15 at 23:22









      user247996user247996

      112




      112






















          1 Answer
          1






          active

          oldest

          votes


















          0














          A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find



          $phi = arctan left( frac{y}{x} right)$



          Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.






          share|cite|improve this answer





















            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "69"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1324387%2fconverting-vector-in-cartesian-to-cylindrical-coordinates%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            0














            A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find



            $phi = arctan left( frac{y}{x} right)$



            Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.






            share|cite|improve this answer


























              0














              A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find



              $phi = arctan left( frac{y}{x} right)$



              Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.






              share|cite|improve this answer
























                0












                0








                0






                A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find



                $phi = arctan left( frac{y}{x} right)$



                Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.






                share|cite|improve this answer












                A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find



                $phi = arctan left( frac{y}{x} right)$



                Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Sep 21 '18 at 8:37









                muralymuraly

                1




                1






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.





                    Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                    Please pay close attention to the following guidance:


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1324387%2fconverting-vector-in-cartesian-to-cylindrical-coordinates%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    Popular posts from this blog

                    Human spaceflight

                    Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

                    張江高科駅