A CAD Tool for Linear Optics Design: A Controls Engineer's Geometric Approach to Hill's Equation

The formulae relevant for the Linear Optics design of Synchrotrons are derived systematically from first principles, a straightforward exercise in Hamiltonian Dynamics. Equipped with these, the relevant "Use Cases" are then captured for a streamlined approach. This will enable professionals -- Software Engineers -- to efficiently prototype & architect a CAD Tool for ditto; something which has been available to Mechanical Engineers since the mid-1960s.