Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have a question about polar coordinates.

It is

[tex]\vec r = \begin{pmatrix}r cos\phi \\ rsin\phi \\ z\end{pmatrix}=r\cdot \vec e_r + z\cdot \vec e_z[/tex]

and than is

[tex]\ddot{\vec r} = (\ddot{r}-r\dot{\phi}^2)\vec e_r + (r\ddot{\phi} +2\dot{r}\dot{\phi})\vec e_{\phi} + \ddot{z}\vec e_z[/tex]

The following I got on the exercise

[tex]m\cdot \begin{pmatrix}\ddot{x} \\ \ddot{y} \\ \ddot{z}\end{pmatrix} =m\cdot \begin{pmatrix}0 \\ 0 \\ -g\end{pmatrix} + 2\lambda \begin{pmatrix}-x\cdot cos^2 \alpha \\ -y\cdot cos^2 \alpha \\ z\cdot sin^2 \alpha\end{pmatrix}[/tex]

I have three components now. One component is an equation(I, II and III).

I also got following hint:

[tex]I:\cos\phi + III: \tan\alpha[/tex]

[tex]z=\frac{r}{\tan \alpha}[/tex]

When I use this hints, I got this:

[tex]\frac{\ddot x}{\cos \phi}+\frac{\ddot{z}}{\tan \alpha} = -\frac{g}{\tan \alpha}[/tex]

Until this point, it should be all clear to me, I guess.

Apprently you will get following, if you go further:

[tex]\frac{(\ddot{r}-r\dot{\phi}^2)cos \phi-(2\dot{r}\dot{\phi}+r\ddot{\phi})\sin \phi}{\cos \phi}+\frac{\ddot{r}}{\tan^2 \alpha}+ \frac{g}{\tan \alpha}=0[/tex]

My Questions:

1. Why is [tex]\ddot{x} = (\ddot{r}-r\dot{\phi}^2)cos \phi-(2\dot{r}\dot{\phi}+r\ddot{\phi})\sin \phi[/tex], apperently?

2. And why is [tex]2\dot{r}\dot{\phi}+r\ddot{\phi}=0[/tex]?

I hope someone can help me with this case.

Kind regards,

Gamdschiee

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Problem with polar coordinates

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Problem polar coordinates | Date |
---|---|

I A problem in combinatorics | Jan 17, 2018 |

B Optimisation problem | Jan 11, 2018 |

I Math papers and open problems | Dec 11, 2017 |

I Interesting question: why is ln(-1) in polar form...? | Mar 30, 2017 |

**Physics Forums - The Fusion of Science and Community**