2
votes
2answers
223 views

Finding the position of a moving point [closed]

A point is moving on a given curve. For example, curve equation is: $$x^2 + y^2 - 10y = 0,$$ which is a circle with $5$ meter radius. If point is on $(0,0)$ at $t = 0$ and is moving on the curve ...
4
votes
1answer
49 views

Geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts

What's the geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts? For example, a skew-symmetric matrix on its own can be interpreted as an infinitesimal rotation. As ...
3
votes
1answer
135 views

Littlewood's orbital joke

In A Mathematician's Miscellany, Littlewood offers this item: To determine the orbit of a planet or comet 3 observations, each of two (angular) co-ordinates and the time t, suffice. It is ...
-1
votes
2answers
95 views

Sketching phase portraits [closed]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
1
vote
1answer
64 views

Is the shadow of the earth coming up almost matching in size with the moon a coincidence?

The fool that I am, today was the first time I wondered how come the shadow of the earth is almost same in size as the moon. I mean, as I was looking at the crescent moon in the evening, it came upon ...
3
votes
2answers
135 views

Distance metric for (infinite) lines in 3D

I would like a metric $d(\;)$ between pairs of (infinite) lines in $\mathbb{R}^3$, with these properties: If two lines $L_1$ and $L_2$ are parallel and separated by distance $x$, then $d(L_1,L_2) = ...
0
votes
1answer
53 views

Woking out directions from forces on a 2D plane

Assume P is a 2D object on a 2D plane. If there are N forces of equal strength pulling P in a particular direction, how can I calculate which direction P will move in? Obviously, if there is only one ...
3
votes
1answer
166 views

Spherical shell enclosing the Earth's surface

What is the minimum thickness of a spherical shell that encloses the Earth's surface? The two spheres are concentric, the outer sphere encloses all the surface (to the highest mountain), and the ...
8
votes
2answers
595 views

Fireworks under inverse-cube gravity

What is the path of a projectile under an inverse-cube gravity law? Imagine that the law of gravity was changed overnight from $F(r) = G m_1 m_2 / r^2$ to $F(r) = G' m_1 m_2 / r^3$. To be ...
9
votes
3answers
309 views

Infinite sequence of nested, falling, colliding spheres

Imagine an infinite collection of nested, concentric spheres, of radius 1, $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$, and so on. Suppose they are somehow suspended in space, fixed on their common ...