- #1
Feles Cestriana
- 4
- 0
The Great Circle et al...
It is certainly intuitively clear that the geodesics on the sphere are the great circles. But, showing that seems to be a bit tricky...
I tried working out the Christoffel symbols, and then plugging that into the differential equations for the geodesics, and aside from it being a bit of a mess, I'm up against a bit of a wall with the system.
Now, perhaps I just need to grind it a little more, and it will all fall out, but, I can't help but wonder if there is a better way to "show" what the geodesics of a surface are.
I've had the same issue with the cylinder...
Any tips, to just point me in the right direction, I'd be most appreciative.
Thanks,
-FC
It is certainly intuitively clear that the geodesics on the sphere are the great circles. But, showing that seems to be a bit tricky...
I tried working out the Christoffel symbols, and then plugging that into the differential equations for the geodesics, and aside from it being a bit of a mess, I'm up against a bit of a wall with the system.
Now, perhaps I just need to grind it a little more, and it will all fall out, but, I can't help but wonder if there is a better way to "show" what the geodesics of a surface are.
I've had the same issue with the cylinder...
Any tips, to just point me in the right direction, I'd be most appreciative.
Thanks,
-FC