Question

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Compare Newtonian, Lagrangian and Hamiltonian formulation and

discuss the advantages and disadvantages of each.​

Answer 1

Each has its own advantages and disadvantages.

Newtonian: directly go to the equations of motion. Cannot easily generalise to relativistic and non classical systems (like classical counterpart of spin).

Lagrangian: ideally suited for relativity, as can be generalised to Lagrangian density. The way to go for quantum field theory. Can easily lead to Hamiltonian mechanics.

Hamiltonian: not manifestly relativistic, but formalism with the best geometric (symplectic) structure. Can be easily generalised to phase spaces that are not R^2n (eg the two sphere). Easily leads to quantization.

Also, both the Lagrangian and Hamiltonian formalism directly relate symmetries of the action and conserved quantities. Eg, invariance under space translation gives momentum conservation, time translation gives energy conservation, rotation symmetry gives angular momentum conservation, etc (Noether's theorem).

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Answer 2

Answer:

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