Ants!

Originally posted by mtthw
Here's how I did it (for the 4 corner case).

The key thing to note is that, due to symmetry, if they start off as a square they are always a square. This means:

- the velocity towards the centre is a constant k/sqrt(2)
- the velocity perpendicular to a line drawn from the centre is a constant k/sqrt(2)

Solving the motion towards the centre is easy. ...[text shortened]... noticed while writing this: it should have been:

theta = -cot(PI/N).ln[1 - kt.sin(PI/N)/a]

hey, mtthw

I hate to be a pain,but can you explain the following statments in more depth

- the velocity towards the centre is a constant k/sqrt(2)
- the velocity perpendicular to a line drawn from the centre is a constant k/sqrt(2)

I'm having trouble coming coming to these conclusions on my own...

thanks
Eric

Originally posted by joe shmo
hey, mtthw

I hate to be a pain,but can you explain the following statments in more depth

- the velocity towards the centre is a constant k/sqrt(2)
- the velocity perpendicular to a line drawn from the centre is a constant k/sqrt(2)

I'm having trouble coming coming to these conclusions on my own...

thanks
Eric

I can try.

Imagine an initial situation like this: ants are at: A (a, 0), B (0, a), C (-a, 0), D (0, -a).
So they're in a square formation (with side a.sqrt(2)).

A is moving towards B. So A is travelling at speed k in the direction from (a, 0) to (0, a).

Which means A's velocity is [-k/sqrt(2), k/sqrt(2)] - the sqrt(2) is there to give it a magnitude of k.

This is made up of a velocity along the X axis (towards the centre) of k/sqrt(2) and a velocity in the Y direction (perpendicular to OA) of k/sqrt(2).

The only assumption there is that the initial configuration is a square. But, because of symmetry, if it starts as a square, it stays as a square. So those are the radial and tangential velocities at any time.

Does that make sense?

Originally posted by mtthw
I can try.

Imagine an initial situation like this: ants are at: A (a, 0), B (0, a), C (-a, 0), D (0, -a).
So they're in a square formation (with side a.sqrt(2)).

A is moving towards B. So A is travelling at speed k in the direction from (a, 0) to (0, a).

Which means A's velocity is [-k/sqrt(2), k/sqrt(2)] - the sqrt(2) is there to give it a magn ...[text shortened]... uare. So those are the radial and tangential velocities at any time.

Does that make sense?

ok,....It didn't sink in that the magnitude of velocity had to be = K. ( hence the algebraic factor of sqrt(2) illuded me.

thanks again😉