Questions tagged [coordinate-systems]

Question 1

In conic sections there are many formulas that involve the three forms: $S$, $T$, and $S_1$, or combinations of these. But I have some questions regarding them. For a general conic: $S \equiv ax^2 + ...

Question 2

This is problem 20.1 from Loring Tu's An Introduction to Manifolds: Let $I$ be an open interval, $M$ a manifold, and {$X_t$} a 1-parameter family of vector fields on $M$ defined for all $t \neq t_0 \...

Question 3

Why standard equation of circle has only three parameters $h$, $k$ and $r$ $(x-h)^2+(y-k)^2-r^2=0$ but the diameter form has $4$ coordinates for the endpoints-$x_1$, $y_1$, $x_2$ and $y_2$? Moreover ...

Question 4

I am studying differentiable topology and I am facing the definition on vector field and Lie bracket. If $M$ is an $m-$manifold and $V,W:T\to TM$ are vector fields on $M$, we define the Lie bracket of ...

Question 5

I'm working with a scriptable 3-D rendering tool that, due to various rounding and binary representation errors in point arithmetic will throw errors at extremely rare but always inopportune times. ...

Question 6

I am reading Analysis on Manifolds by James R. Munkres. I can’t clearly understand the following passage by the author. It leaves me with a vague, unsettled feeling. On p.171 in this book: Definition....

Question 7

Take a grid in an arbitrary number of dimensions. I construct a graph kernel to define the connectivity of the grid, and apply that kernel to the grid to create a weighted digraph. I Construct the ...

Question 8

I'm an highschool student who just got into coordinate geometry. the one thing that i noticed is whenever proof for centroid formula pops up there always is the additional data manually added that ...

Question 9

I have a problem with a hacky solution that's been bugging me for a long time. I'm hoping someone can help me with a proper solution and put my mind at peace. Imagine you have a computer screen, where ...

Question 10

I have been thinking recently about the transition from abstract mathematical objects and vector spaces to visual represenations of these objects. In particular, I was thinking about our typical ...

Question 11

Is there a 3D coordinate transform which turns rotation in cartesian coordinates into translation in the transformed coordinate system? It would be sufficient if the transformation has the desired ...

Question 12

I have a vector field $V$ defined in $\mathbb{R}^3$ which is curl free and divergence free, \begin{align} \nabla \times V &= 0 \\ \nabla \cdot V &= 0 \end{align} The curl free condition means ...

Question 13

In the theory of generalized (curvilinear) coordinates, usually one defines coordinates first, e.g. $(u^1,u^2,u^3)$, then a position vector $\mathbf{r}(u^1,u^2,u^3)$, and finally the basis vectors, $$ ...

Question 14

When I'm watching One Piece (animation), I'm thinking about how can I create a curve like this in a coordinate system First, I think about Archimedean Spiral$$r(\theta) = a + b\theta$$ but after ...

Question 15

In "Calculus With Analytic Geometry" , the author (G.F. Simmons) says the following, while explaining Polar Coordinates: Distance is given by the directed distance $r$, measured out from ...

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Questions tagged [coordinate-systems]

Usage Of $T, S $ and $ S_1$ [closed]

The limit of a family of vector fields is independent of chart

I am having difficulty in reconciling the standard and diameter forms of equation of circle. [closed]

Lie bracket and independence on the coordinates

How to overcome Cartesian/Polar round trip anomalies in 64-bit IEEE floating-point numbers

Is it possible to define the concept of a right-handed coordinate system (not a right-handed frame) mathematically? Munkres's Analysis on Manifolds.

how to construct a volume element of a coordinate system warped by a kernel function

why centroid is located on 2:1 ratio of medians

Converting a 2d Grid coordinate to screen coordinates?

Is the way we draw coordinate axes arbitrary and if not what is the argument for why it isn't?

3D coordinate transform that turns rotation into translation

Directional derivative of conservative vector field

Calculating coordinates out of basis vectors

Make a curve that's similar to the eyebrow in a coordinate system

Terminal side in polar coordinates

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