Damped Equilibrium Muscle Model

[Rachid Ramadan]

Hi,

How does the concrete computation of the force for the damped muscle model work?
The equilibrium equation is given by:

(a*fl(f^M)*fv(v^M)+fpe(l^M)+beta*v^M)*cos(alpha)-ft(l^T)=0

Do I, similar to the undamped version, need to solve the equation for v^M (with fl, fv,ft, fpe from previous timestep ) and then integrate v^M to get a new l^M that I in turn can use as the length for the next timestep?

Best, Rachid

[Thomas Uchida]

As described in Section 2.3 of Millard et al. (2013), the damping term allows you to solve the equilibrium equation for v^M using a derivative-based root-finding algorithm (i.e., you don't need to isolate v^M and invert the force--velocity curve). Muscle fiber length l^M is still a state.

Here's the paper: Millard, M., Uchida, T., Seth, A., Delp, S.L. Flexing computational muscle: modeling and simulation of musculotendon dynamics. ASME Journal of Biomechanical Engineering 135(2):021005, 2013. https://nmbl.stanford.edu/publications/ ... rd2013.pdf

Here's the code on GitHub:
- https://github.com/opensim-org/opensim- ... umMuscle.h
- https://github.com/opensim-org/opensim- ... Muscle.cpp