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Hierarchical enumeration of cases
1: Two objects, X and Y, collide.
1.1: Y is either moving freely or swung by an agent.
1.1.1: X moving freely
1.1.1.1: Y is much lighter than X.
Then X's motion is hardly affected by the collision.
1.1.1.2: Y is at least comparable in weight to X
1.1.1.2.1: Y hits X on center. (i.e. the center of X is approximately
a non-negative sum of normals to the points of contact.)
1.1.1.2.1.1: Y hits X squarely (i.e. the line along the direction of relative
motion from the center of X lies within the normals of the point of contact.
Then X's motion will gain a substantial component along the center
line.
1.1.1.2.1.1.1: Y is much heavier than X.
Then Y's motion is only slightly affected by the incident
1.1.1.2.1.1.2: Y's weight is comparable to X's.
Then Y's motion is substantially affected by the incident. If Y
is in free fall, then the change to Y's motion is given by these same rules
(substituting Y for X and vice versa). If Y is under the control
of an external agent, then Y's behavior depends on the characteristics
of the agent.
1.1.1.2.1.2: Y glances off X.
Then X's motion will gain a small amount along the center. X may
also gain some spin along the direction of Y's motion.
1.1.1.2.2: Y hits X off center. (Note: This can't happen if X is a sphere.)
1.1.1.2.2.1: Y hits X squarely.
Then X's motion will gain a substantial component along the direction
of relative motion and a spin around the center in the direction of the
applied torque. Y's motion is affected as described under 1.1.1.1.1.1.
1.1.1.2.1.2: Y glances off X.
Then X's motion will gain a small amount along the center, and X will
also gain some spin along the direction of Y's motion.
1.1.2: X is in a stable position on the ground.
1.1.2.1: X is in a very stable position.
1.1.2.1.1: In horizontal projection, Y hits X on center
1.1.2.1.1.1: In horizontal projection, Y hits X squarely.