What are Lagrangian and Hamiltonian mechanics?
Lagrangian exists as the difference between kinetic and potential energy.
Lagrangian is found by the Italian mathematician in the year 1788.
Lagrangian represented by cartesian coordinates.
Hamiltonian is the mathematically sophisticated formulation of classical mechanics.Why is Lagrangian instead of Hamiltonian?
The Standard Model of particle physics is typically expressed using a Lagrangian rather than a Hamiltonian because the Lagrangian formalism is more naturally suited for describing systems with constraints, such as those found in particle physics.
What is Hamilton's principle and Lagrange's equation?
Suppose we have two systems A and B separated by large distances so they do not interact with each other.
Then the Lagrangian for this composite system must consist of separate parts for each, i.e., L(A + B) = L(A)+ L(B).
Furthermore, multiplying L by some constant would change nothing in the equations so far.- However, the Hamiltonian is fundamental in quantum mechanics and is often (not always) equal to the energy.
However, in relativistic quantum mechanics the Lagrangian seems to be the fundamental quantity.
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