# Tagged Questions

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### Show that the parameterized curve is a periodic solution to the system of nonlinear equations

First I tried to convert the system to polar coordinates. This only made things worse (unless I made some idiotic mistake). Can I plug in the given ellipse (rectangular coordinates) into the ...
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### How to prove this ODE system is stable at origin?

A dynamical system in polar coordinates is: $$\Theta'=1, r'= r^2\sin(1/r), r>0, r'=0\mbox{ if }r =0.$$ How to show this is stable at origin? Intuitively, I really can't believe it because I ...
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### Pure differential equation whose solution is a siluroid?

I am trying to find a differential equation for the siluroid that DOES NOT contain explicitly $\theta$, $\sin\theta$, or $\cos\theta$, but only $\rho$, $\dot\rho$, $\ddot\rho$. The siluroid equation ...
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### Qualitative analysis of an ordinary differential equation in polar coordinates

I want to draw the integral curves of the differential equation in polar coordinates $(\theta, \rho)$ $\frac{d\rho}{d\theta}= \rho^3-6\rho^2+8\rho$ At first I thought it would suffice to analyse ...
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### Diff eq. transformation polar coordinates

I have $(x',y')=(x-y-x(x^2+y^2)+\frac{xy}{\sqrt{x^2+y^2}},x+y-y(x^2+y^2)-\frac{x^2}{\sqrt{x^2+y^2}} )$ Now I want to use polar coordinates $(x,y)=(r\cos(t),r\sin(t))$ to get ...
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### Explain Dot product with Partial derivatives in Polar-coordinates

Related to page 819 prob 4 in this book. I am incorrectly calculating the left-hand-side (def. LHS), some newbie error with commutativity probably. Ideas? Errors? I propose ...
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### Orthonormal vectors in Polar coordinates, show $\hat{e}_R=\frac{(x,y,z)}{r}$

Definitions Unit vector has length 1. Orthonormal vectors are orthogonal and unit vectors. RobJohn's suggestions for the basis in polar coordinates, here, satisfy the criteria but how can ...
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### Explain Triangle perimeter in polar coordinates

The question is to give a formula in $x$ and $y$ that gives all three sides of an equilateral triangle. The formula should not be true for points that are not part of the perimeter of the triangle. ...
### Why is $dy dx = r dr d \theta$ [duplicate]
Possible Duplicate: Explain $\iint \mathrm dx\mathrm dy = \iint r \mathrm d\alpha\mathrm dr$ I'm reading the proof of Gaussian integration. When we change to polar coordinates, why do we ...