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4. The inertial terms in the dynamic equations which are products of the zero partial derivative matrices are not computed (since they are also zero) and the constant matrices are explicitly assigned, reducing computational effort. 5 Massless Leg Model A massless leg model is formulated by reallocating leg inertias to the body and updated body parameters are calculated for the first iteration of each timestep. 6). The parallel axis theorem  is not applicable for reallocating leg inertias because shoulder joint rotations skew the link axes relative to the body axes.
Existing ODE solution software assumes the equations are specified in a standard first order form. The second order equations of motion for a mechanical system must be transformed into an equivalent first order form for subsequent solution with these programs. The required transformation is dependent on the original form of the equations. Calculating solutions for legged locomotion on natural terrain using available ODE packages requires a transformation of the equations of motion (after substitution of any specified joint trajectories) into standard DAE form  and the subset of differential equations converted to first order form.
5 Massless Leg Model A massless leg model is formulated by reallocating leg inertias to the body and updated body parameters are calculated for the first iteration of each timestep. 6). The parallel axis theorem  is not applicable for reallocating leg inertias because shoulder joint rotations skew the link axes relative to the body axes. Application to a Prototype Walking Machine 49 Leg contributions to the body inertial parameters are calculated by specifying leg member positions in the body coordinate frame and substituting these expressions into the body inertia equations for subsequent integration.
1934 General Motors GM Fisher Body Service Manual by General Motors