Constraint Compliance and Spook Damping

AGX Dynamics performs numerical calculations by solving equations of motion and constraint conditions simultaneously. When constraint conditions are not satisfied, they must be satisfied through some method. AGX Dynamics uses a viscoelastic (spring-damper) model for this purpose. However, due to the relationship between formulation and numerical calculation, the viscoelastic model is slightly transformed, with the following relationships:

F = -Kx - Dv   # Spring Damper model
F = -1/Cx - Dv # Replace K with compliance 1/C
CF = -x - CDv  # Multiply C^2 at both sides
CF = -x - hv   # Merge CD to h

K = 1/C        # Spring Coefficient [N/m] or [Nm/rad]
C = 1/K        # Compliance [m/N] or [rad/Nm]

h = CD = D/K   # Spook Damping [s]
D = hK = h/C   # Damping Coefficient [Ns/m] or [Nm s/rad]