Equations of Motion

The system equation of motion employed in ODE is

which is clearly an explicit time-stepping scheme. However, the constraint equation is expressed implicitly.

Eq. (1) and (2) can be combined to be

Eq. (3) can be described as a “hybrid” time-stepping scheme. If there are lack of contraints, the equation will be susceptible to instability. Furthermore, cfm is introduced into the LHS of Eq. (3)

Eq. (4) is then solved by the LCP subroutine to yield lambda. Finally,
update velocities from Eq. (1),

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