Compliance and spook damping of constraints

AGX Dynamics performs numerical calculation of simultaneous equations which have equation of motion and constraints.

When the constraint condition is not satisfied, it is necessary to satisfy the condition in some way,

AGX Dynamics uses a viscoelasticity (spring damper) model to satisfy the constraint condition.

Notice that, for formulation and numerical calculation, AGX Dynamics transforms the viscoelastic model as follows and uses parameters such as compliance and spook damping.

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]