Transformation Theory of Birkhoff’s Equations

Abstract

As is now familiar, an objective of this volume is to establish methodological foundations for the treatment of the most general known class of local interactions, those of the variational non-self-adjoint type. The interactions can be essentially reduced to a superposition of action-at-a-distance, potential forces F^SA, and contact forces F^NSA for which the notion of potential energy is inapplicable, according to the systems

$${m_{a}}{_{{ka}}} - f_{{ka}}^{{SA}}\left( {t,r{\text{,}}} \right) - F_{{ka}}^{{NSA}}\left( {t,r{\text{,}}} \right) = 0,a = 1,2,...,N,k = x,y,z. $$

((1))

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