The sphere rotates underneath the particle.
BSEditor: Simulation of frictionless motion of a particle that is constrained to follow the surface of a perfect Sphere. The sphere rotates underneath the particle, but since there is no Friction, and the sphere is perfectly spherical, the motion of the particle is not influenced by the sphere. The particle is released from co-rotating motion.

The simulation shows simultaneously the trajectory with respect to the inertial coordinate system, and the trajectory as seen from a point of view that is co-rotating with the sphere.

When the Play button is pressed the sphere starts to rotate with the particle co-rotating at an initial latitude. The particle remains co-rotating until the Release/Launch button is pressed. On pressing the Release/Launch button the particle commences to MOVE along the great Circle that is tangent to the initial latitude.

The input fields:

System rotation rate. Inputting a larger value speeds up the evolution, and inputting a smaller value slows down the simulations evolution. Inputting zero as system rotation rate makes the simulation behave differently. Then the motion relative to the sphere is the same in both panels, so you can compare with the case of a rotating sphere.

Starting latitude. This value is in degrees.

Release/launch velocity. This value is not expressed in units of velocity; its a percentage. At each latitude it is the percentage of the velocity for co-rotating with the sphere at that latitude. You can input any positive or Negative value for the Release/launch velocity. The smoothest release is when you input a value of zero for the Release/launch velocity.

Object angular velocity. The angular velocity of the particle as it moves along a great circle. System rotation rate and Object angular velocity are scaled the same, so if you input the value 1 for the Object angular velocity then the particle will complete a great circle in one full rotation of the system. you can free download Great Circles Model now.