The Physics of Oscillations and Waves pp 161-180 | Cite as

# Matrices—Rotations—Eigenvalues and Eigenvectors—Normal Coordinates

Chapter

## Abstract

In the preceding chapter we encountered the problem of uncoupling the simultaneous equations of motion arising from the Lagrangean .

$$ L = T - V = \frac{1}
{2}\sum\limits_{m,n} {T_{mn} \dot s_m \dot s_n - \frac{1}
{2}} \sum\limits_{m,n} {V_{mn} s_m s_n .} $$

(10.1)

## Keywords

Diagonal Element Configuration Space Diagonal Form Secular Equation Column Matrix
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## Notes

- 1.For a full and careful treatment of matrix algebra, the reader is referred to books on higher algebra; for example, Bocher, M.
*Introduction to Higher Algebra*. New York: Macmillan, 1924.Google Scholar - 2.The properties of systems of linear algebraic equations are discussed in Arfken, G.
*Mathematical Methods for Physicists*. 2d ed. New York: Academic Press, 1970. Belcher,*Introduction to Higher Algebra*. Courant, R., and D. Hilbert.*Methods of Mathematical Physics*. New York; Interscience, 1953; also Margenau, H. and G. M. Murphy.*The Mathematics of Physics & Chemistry*. New York: Van Nostrand, 1943.Google Scholar - 3.It is customary to discuss the normal-coordinate transformation as a single process rather than as a sequence of three operations. (See, for example, Goldstein, H.
*Classical Mechanics*. 2nd ed. Reading, MA: Addison Wesley, 1980.Google Scholar

## Copyright information

© Springer Science+Business Media New York 1997