Approach In general, we can extend the Filter class to add whatever behavior we want, as long at the output is an influence on a single channel.
For example, we can have channels that are used to set changing gravity, mass, or attraction to a point or another actor.
Gravity This should be fairly simple. We also want the floor to act as a block (so the character doesn't sink down forever!).
Squash and Stretch At the lowest (geometric) level, this is probably best done as animation, not as physics. We can use higher level procedures to steer this though.
Mass/Spring wobbling Extend filters, and create methods that use simple f=f'' (position = 2nd derivative), with controllable damping at each vertex.