Abstract: Equilibrium forces and momentum are calculated using character skeleton node graphs having variable root nodes determined in real time based on contacts with fixed objects or other constraints that apply external forces to the character. The skeleton node graph can be traveled backwards and in so doing it is possible to determine a physically possible reaction force. The tree can be traveled one way to apply angles and positions and then traveled back the other way ‘to calculate’ forces and moments. Unless the root is correct, however, reaction forces will not be able to be properly determined. The adaptive skeleton framework enables calculations of reactive forces on certain contact nodes to be made. Calculation of reactive forces enables more realistic displayed motion of a simulated character.