As described in Inverse Dynamics, the motion of the model is completely defined by the generalized positions, velocities, and accelerations. The Static Optimization Tool uses the known motion of the model to solve the equations of motion for the unknown generalized forces (e.g., joint torques) subject to one of the following muscle activation-to-force conditions:

ideal force generators:

\sum_{m=1}^{n} (a_m F_m^0) r_{m,j} = \tau_j |

or, constrained by force-length-velocity properties:

\sum_{m=1}^{n} [a_m f(F_m^0, l_m, v_m) ] r_{m,j} = \tau_j |

while minimizing the objective function:

J = \sum_{m=1}^{n} (a_m)^p |

where *n* is the number of muscles in the model; *a*_{m} is the activation level of muscle *m *at a discrete time step; is its maximum isometric force; *l _{m}* is its length;

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