Matrices—Rotations—Eigenvalues and Eigenvectors—Normal Coordinates

  • Ingram Bloch


In the preceding chapter we encountered the problem of uncoupling the simultaneous equations of motion arising from the Lagrangean
$$ L = T - V = \frac{1} {2}\sum\limits_{m,n} {T_{mn} \dot s_m \dot s_n - \frac{1} {2}} \sum\limits_{m,n} {V_{mn} s_m s_n .} $$


Diagonal Element Configuration Space Diagonal Form Secular Equation Column Matrix 
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  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

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© Springer Science+Business Media New York 1997

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  • Ingram Bloch

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