Patent ID: 7433144

Claim:
A method of generating a position-velocity table for a dynamic system, the method comprising the steps of; modeling the dynamic system in terms of partial fraction expansion equations; integrating the partial fraction expansion equations forward in time so as to generate a trajectory for the dynamic system; and storing the trajectory for the system in the position-velocity table, wherein the partial fraction expansion equations which model the dynamic system comprise: Finalpos = ∑ i = 1 N ⁢ ⁢ V i ⁢ A ⁢ ⁢ Δ ⁢ ⁢ t 0 = ∑ i = 1 N ⁢ ⁢ V i ⁢ Ab b - a ⁢ ( ⅇ - a ⁡ ( T end - T i + Δ ⁢ ⁢ t ) - ⅇ - a ⁡ ( T end - T i ) ) 0 = ∑ i = 1 N ⁢ ⁢ V i ⁢ Aa a - b ⁢ ( ⅇ - b ⁡ ( T end - T i + Δ ⁢ ⁢ t ) - ⅇ - b ⁡ ( T end - T i ) ) , where Finalpos is the final position of a component of the dynamic system, T end corresponds to a time at which Finalpos is reached, A, a and b are based on the system parameters, Vi are inputs to the system, Ti are the times at which Vi are input and t is a time interval at which Vi are input.