The Lagrangian represents the difference between kinetic and potential energy, while the Hamiltonian is the sum of these energies. The calculation of the Lagrangian is crucial as it allows for the derivation of equations of motion when the action is extremized. Specifically, the action is defined as the time integral of the Lagrangian, which leads to a comprehensive description of physical systems. Understanding these concepts is essential for analyzing motion in classical mechanics.
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Why do we do anything in physics? We do it because it gives a good description of what we can observe.avito009 said:Why do we calculate the lagrangian or hamiltonian?
No, when the action is extremised (i.e., maximised, minimised, or finding a saddle point) we find the equations of motion. The action is the time integral of the Lagrangian.avito009 said:When the Lagrangian is maximised it gives equations of motion.