The Maggi and Kane equations of motion are valid for systems with only nonholonomic constraints, but may fail when applied to systems with holonomic constraints. A tangent space ordinary differential equation (ODE) extension of the Maggi and Kane formulations that enforces holonomic constraints is presented and shown to be theoretically sound and computationally effective. Numerical examples are presented that demonstrate the extended formulation leads to solutions that satisfy position, velocity, and acceleration constraints for holonomic systems to near computer precision.

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