An Analogy Between the Variational Principles of Reactor Theory and those of Classical Mechanics

A formal parallelism is shown to exist between two classical variational principles governing the time behavior of mechanical systems and two principles relating to the λ-mode eigenvalue problem of neutron group diffusion theory. By identifying the space variable with the time variable and space derivatives (gradients and divergences) with time derivatives, the ‘usual’ variational principle of diffusion theory is shown to be analogous to Hamilton's principle and the diffusion equations are analogous to the Lagrange equations. Hamilton's canonical equations are then analogous to the diffusion equations in first-order form, and the analog of the principle involving the canonical integral is a principle closely related to one proposed recently by Selengut and Wachspress.