## Abstract

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.

### Keywords

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### References

- For a thorough discussion of Lagrangian equations, see Greenwood (1977). For influence coefficients (Sec. 2.3), see Fung (1955), and Fung (1965). For aerodynamic loading, see Fung (1955). For muscle mechanics, see Fung (1981).Google Scholar
- Bean, J.C., Chaffin, D.B., and Schultz, A.B. (1988). Biomechanical model calculation of muscle contraction forces: a double linear programming method.
*J. Biomech.***21**: 59–66.CrossRefGoogle Scholar - Bellman, R.E. (1970).
*Introduction to Matrix Analysis*, 2nd ed. McGraw-Hill, New York.MATHGoogle Scholar - Camana, P.C., Hemami, H., and Stockwell, C.W. (1977). Determination of feedback for human posture control without physical intervention.
*J. Cybernet.***7**: 199.MathSciNetCrossRefGoogle Scholar - Caughey, T.K. (1960). Classical normal modes in damped linear dynamic systems.
*J. Appl. Mech.***27**: 269–271.MathSciNetADSMATHCrossRefGoogle Scholar - Chao, E.Y.S. (1980). Justification of triaxial goniometer for the measurement of joint motion.
*J. Biomech.***13**: 989–1006.CrossRefGoogle Scholar - Chao, E.Y.S. and Morrey, B.F. (1978). Three-dimensional rotation of the elbow.
*J. Biomech.***11**: 57–74.CrossRefGoogle Scholar - Fung, Y.C. ( 1955, 1969).
*The Theory of Aeroelasticity*. Wiley, New York. Revised, Dover Publications, New York.Google Scholar - Fung, Y.C. (1965).
*Foundations of Solid Mechanics*, Prentice-Hall, Englewood Cliffs, N.J. Ghista, C.N. (1982).*Osteoarthromechanics*. McGraw-Hill, New York.Google Scholar - Greenwood, D.T. (1965).
*Principles of Dynamics*. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar - Greenwood, D.T. (1977).
*Classical Dynamics*. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar - Grood, E.S. and Suntay, W.J. (1983). A joint coordinate system for the clinical description of three-dimensional motions: Application to the knee.
*J. Biomech. Eng.***105**: 136–144.CrossRefGoogle Scholar - Huston, R.L. and Perrone, N. (1980). Dynamic response and protection of the human body and skull in impact simulation. In
*Perspective in Biomechanics*.**(H**. Reul, D.N. Ghista and G. Rau, eds.), Vol. 1, Part B, pp. 531–571, Harwood Academic Publishers, New York. Kane, T.R. (1968).*Dynamics*. Holt, Rinehart, and Winston, New York.Google Scholar - McGhee, R.B. (1980). Computer simulation of human movements. In
*Biomechanics of Motion*( A. Morecki, ed.), Springer-Verlag, Wien and New York, pp. 41–78.Google Scholar - Mizrahi, J. and Susak, Z. (1982). In vivo elastic damping response of the human leg to impact forces.
*J. Biomech. Eng.***104**: 63–66.CrossRefGoogle Scholar - Nashner, L.M. (1971). A model describing vestibular detection of body sway motion.
*Acta Otolaryng*.**72**: 429–436.CrossRefGoogle Scholar - Pauwels, F. (1980).
*Biomechanics of the Locomotor Apparatus*. (Trans. from the German by P. Magnet and R. Furlong) Springer-Verlag, New York.CrossRefGoogle Scholar - Pedotti, A. (1980). Motor coordination and neuromuscular activities in human locomotion. In
*Biomechanics of Motion*( A. Morecki, ed., Springer-Verlag, New York, pp. 79–129.Google Scholar - Rayleigh, Baron, John William Strutt (1894).
*The Theory of Sound*. Republished by Dover, New York, Vol. 1, p. 131.Google Scholar - Roth, B. (1967). Finite position theory applied to mechanism synthesis.
*J. Appl. Mech.***34**: 599–606.ADSCrossRefGoogle Scholar - Schultz, A.B., Anderson, G.B.J., Haderspeck, K., Örtengren, R., Nordin, M., and Björk, R. (1982). Analysis and measurement of lumbar trunk loads in tasks involving bends and twists.
*J. Biomech.***15**: 669–675.CrossRefGoogle Scholar