... chain rule:∂H∂pi=˙qi+n j= 1p j ∂ ˙q j ∂pi−∂L∂ ˙q j ∂ ˙q j ∂pi=˙qi(1.1.10) and ∂H∂qi=n j= 1p j ∂ ˙q j ∂qi−∂L∂qi−n j= 1∂L∂ ˙q j ∂ ˙q j ∂qi= −∂L∂qi, (1.1.11)where ... subsequent chapters.Lagrangian and Hamiltonian Mechanics. Mechanics has two mainpoints of view, Lagrangian mechanics and Hamiltonian mechanics. In one sense, Lagrangian mechanics is more fundamental ... quantum mechanics, control theory, and other areas of physics, engineering and evenchemistry and biology. Clearly mechanics is a large subject that plays afundamental role in science. Mechanics...