Editing Analytical mechanics (section)

===Generalized coordinates and constraints===
{{Main | Generalized coordinates}}
In [[Newtonian mechanics]], one customarily uses all three [[Cartesian coordinates]], or other 3D [[coordinate system]], to refer to a body's [[position (vector)|position]] during its motion. In physical systems, however, some structure or other system usually constrains the body's motion from taking certain directions and pathways. So a full set of Cartesian coordinates is often unneeded, as the constraints determine the evolving relations among the coordinates, which relations can be modeled by equations corresponding to the constraints. In the Lagrangian and Hamiltonian formalisms, the constraints are incorporated into the motion's geometry, reducing the number of coordinates to the minimum needed to model the motion. These are known as ''generalized coordinates'', denoted ''q<sub>i</sub>'' (''i'' = 1, 2, 3...).<ref>Kibble, Tom, and Berkshire, Frank H. "Classical Mechanics" (5th Edition). Singapore, World Scientific Publishing Company, 2004.</ref>{{rp|231}}