If normal force is the only interaction between particel and torus, there is a minimum velocity to keep the particle always attached to the torus surface.
The coordinate of the particle is

x=(R+ r\cos\theta) \cos \phi
y=(R+ r\cos\theta) \sin \phi
z=r \sin\phi

Due to symmetry, \frac{d\phi}{dt}=\frac{2 \pi}{T} is a constant, and due to gravity \frac{d^2\theta}{dt^2}=-\frac{g\cos\theta}{r}

You can adjust mass m (no effect on the motion), both radius R and r with slider.

/htdocs/ntnujava/ejsuser/2/users/ntnu/fkh/particleontorussurface_pkg/particleontorussurface.propertiesFull screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
Download EJS jar file(1608.2kB):double click downloaded file to run it. (21 times by 10 users) , Download EJS source (8 times by 2 users) View EJS source