[nwwqhvem] curving spinning projectiles in 2D

consider an idealized hockey puck.  it moves in 2D with a constant velocity -- a straight line.

if the puck is spinning (paint a spiral pattern on it to see its spin rate), let it travel a curved path.  this is intentionally unrealistic: we wish to invent physics (e.g., for a game) to make this possible, in particular, to define a trajectory that depends on the puck's translational and rotational momentum.

inspired by Malladus in Zelda Spirit Tracks.

real physics-inspired model of friction: each point on the underside of the puck encounters friction force in the direction exactly opposite to that point's velocity.  friction could be constant, or proportional to speed, or proportional to some constant power of speed.  exponent could be negative: less friction at higher speed.  maybe high speed melts the ice underneath the puck and creates a low-friction cushion of water.

integrate the frictional forces over (under) the area of the puck, then (this is highly unrealistic) only keep the component of the force perpendicular to the motion of the puck.  perpendicular force induces circular motion, leaving speed unchanged.  a spinning projectile, if unimpeded, will return to its origin like a boomerang.  (maybe this is undesirable?)  a non-spinning projectile travels in a straight line forever.

should a spinning projectile curve in the direction it is spinning, or the other way?  we are inventing physics, so this is an aesthetic decision.  for a given spin rate, should larger projectiles curve more, less, or the same?

invent a game, e.g., Pong, that encourages players to learn to extrapolate curved trajectories based on observed spin rate and velocity.