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Matrices—Rotations—Eigenvalues and Eigenvectors—Normal Coordinates

  • Ingram Bloch

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 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. 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. 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

Authors and Affiliations

  • Ingram Bloch

There are no affiliations available

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