  We propose a simple and practical approach for incorporating the effects of
muscle inertia, which has been ignored by previous musculoskeletal simulators
in both graphics and biomechanics. We approximate the inertia of the muscle by
assuming that muscle mass is distributed along the centerline of the muscle. We
express the motion of the musculotendons in terms of the motion of the skeletal
joints using a chain of Jacobians, so that at the top level, only the reduced
degrees of freedom of the skeleton are used to completely drive both bones and
musculotendons. Our approach can handle all commonly used musculotendon path
types, including those with multiple path points and wrapping surfaces. For
muscle paths involving wrapping surfaces, we use neural networks to model the
Jacobians, trained using existing wrapping surface libraries, which allows us
to effectively handle the Jacobian discontinuities that occur when
musculotendon paths collide with wrapping surfaces. We demonstrate support for
higher-order time integrators, complex joints, inverse dynamics, Hill-type
muscle models, and differentiability. In the limit, as the muscle mass is
reduced to zero, our approach gracefully degrades to traditional simulators
without support for muscle inertia. Finally, it is possible to mix and match
inertial and non-inertial musculotendons, depending on the application.
