In the preceding chapter we described motion in the Newtonian form. An animal is considered to be a collection of particles, and particle movement is expressed in terms of displacement, velocity, acceleration, external forces, and forces of interaction between particles. In application to biomechanics, one finds that the terms F IJ in Eq. (1.1:7), that describe the mutual interaction between particles, are the most troublesome. For example, in the analysis of human locomotion, we must know the forces in all the muscles of the legs. But the human musculoskeletal system is highly redundant and the determination of the forces in the muscles is one of the most difficult problems in biomechanics (see Sec. 2.8 infra). Hence there is a need for a method that does not require such detailed information. The method of Joseph Louis Lagrange (1736–1813) offers such an alternative in terms of work and energy. If the kinetic and potential energies are known as functions of the generalized coordinates and their derivatives with respect to time, and if the work done by the external forces can be computed when a generalized coordinate changes, then the equations of motion can be written down.
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