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MathematicalPhysicist

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And why does it seem that LH make solutions to be a lot more easier than Newtonian methods, and is it always this way?

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- #1

MathematicalPhysicist

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And why does it seem that LH make solutions to be a lot more easier than Newtonian methods, and is it always this way?

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The reason for this is that it most easily allows to study symmetries of the fundamental laws of nature, such as space-time symmetries (Galileo, Poincare, general covariance) and external symmetries leading to conservation laws for engery, momentum, angular momentum, center-of-mass velocity, and various charge-like quantities (electrical charge, baryon number, lepton number, etc.), respectively.

Of course, on the classical (i.e., non-quantum) level of point-particle mechanics, the action principle is equivalent to the Newton (or relativistic if necessary) equations of motion for the particle, and you can of course write down this equations from the very beginning.

What makes the action principle more convenient from a practical point of view is that it is way easier to express the action (or the Lagrangian/Hamiltonian) of the system in general coordinates, adapted to the problem at hand, than using directly the equations of motion and performing the transformation from Cartesian to generalized coordinates.

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And why does it seem that LH make solutions to be a lot more easier than Newtonian methods, and is it always this way?

If by "classical" you mean

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