Design or Reference Orbit

The reference orbit consists of a series of straight line segments and circular arcs. It is defined under the assumption that all elements are perfectly aligned along the design orbit. The accompanying tripod of the reference orbit spans a local curvilinear right handed coordinate system $(x,y,s)$. The local $s$-axis is the tangent to the reference orbit. The two other axes are perpendicular to the reference orbit and are labelled $x$ (in the bend plane) and $y$ (perpendicular to the bend plane).