Foot skate solver
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This paper describes how to solve a famous problem with motion capture editing.  
When motion captured data is edited, the feet may not stay on the ground   
at each foot step, it may slide (skate). The solution only takes into   
account the bottom half of the skeleton. There are several steps to   
correct footskate. First, the required position for the foot is calculated.  

Next, the foot is manipulated as to put it in the correct orientation.   
The leg is then manipulated to make the ankle as close as possible to its final   
destination. Finally, the leg is stretched to put the foot exactly where we need it.  
  
  
The last step is a little controversial, because if we are animating a mesh,  
the behavior of stretching a bone is undefined on the skin (AFAIK).  
  
There are lots of math equations that I didn't fully understand in this paper.   
I wish I could see more explanations for these equations.