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Feldoh
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Hey I was just wondering what the differences between the three forms of mechanics were. I've only studied basic Newtonian mechanics so I'm not really sure about the other two. Could anyone elaborate?
The main difference between these three mechanics is the approach they use to describe the motion of a system. Newtonian mechanics is based on the laws of motion and forces, while Lagrange mechanics uses the concept of energy and generalized coordinates, and Hamiltonian mechanics uses the concept of energy and momentum.
Hamiltonian mechanics is considered the most comprehensive as it can be applied to both classical and quantum mechanical systems, and it takes into account the concept of phase space and the symmetries of a system.
Generalized coordinates allow for a more efficient and concise description of the motion of a system, as they are independent of the specific physical coordinates and can be chosen to simplify the equations of motion.
One advantage of using Hamiltonian mechanics is that it provides a more elegant and unified description of a system's motion, as it combines the concepts of energy and momentum. It also allows for the use of symmetries to simplify the equations of motion.
Yes, all three mechanics can be applied to a wide range of systems, from simple particles to complex systems such as the motion of planets in a solar system. However, the most appropriate mechanics to use may depend on the specific characteristics of the system being studied.