Question

Path of a stone in a rotating frame. Please help me.

Answer 1

A stone is thrown inside a room which rotates about a central vertical axis Oz with constant angular velocity ω. The axes Ox, Oy are fixed along the floor in the room. It holds that \[\ddot x-2 \omega\dot y-\omega^2x=0\]
\[\ddot y+2 \omega\dot x-\omega^2y=0\]
\[\ddot z=-g\].
Also, it holds that \[\ddot \xi+2i \omega\dot \xi-\omega^2 \xi=0 \ where \ \xi=x+iy, i=\sqrt{-1}\]. If stone started to move from point \[\vec r(0)=(a,0,h) \ with \ velocity \ \dot r'=(Vcos \alpha,0,Vsin \alpha)\] relative to the rotating room, find a path of the stone in the form r=r(t) and compare it with path relative to the surface of the Earth.

Answer 2

http://www.maths.tcd.ie/

Answer 3

what about this?