Accessible study provides detailed account of the Hamiltonian treatment of aberration theory in geometrical optics. Many classes of optical systems defined in terms of their symmetries. Detailed solutions. 1970 edition.

Introduction -- Characteristic functions -- Symmetries and regularity -- The symmetric system (part I) -- The symmetric system (part II) -- Symmetric systems with additional symmetries -- The semi-symmetric system -- Systems with translational symmetry, and plane-symmetric systems -- Systems with toroidal symmetry -- Chromatic defects of the image -- Anisotropy -- The computation of aberration coefficients.

Publisher Description

It is by no means easy for the applied mathematician to decide how much importance he should attach to the more abstract and aesthetic side of his work ... To all appearances, Sir William Rowan Hamilton (1850-1865) attached little importance to the practical applications of his method, and it was only with the publication of his Mathematical Papers that it was possible to form a more correct and balanced judgement of Hamilton as an applied mathematician.

This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and well-chosen exercises. For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton–Jacobi equation, and the Liouville Theorem on solutions of the Hamilton–Jacobi equation. Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.