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franznietzsche
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Does anyone know of a good online resource on Lagrangian and Hamiltonian mechanics?
Originally posted by Dimitri Terryn
Try this. It's not exactly beginner's stuff, but it's not hard either
http://www.courses.fas.harvard.edu/~phys151/
Hamiltonian and Lagrangian Mechanics are two different mathematical frameworks used to describe the dynamics of a physical system. Lagrangian Mechanics uses generalized coordinates to describe the motion of a system, while Hamiltonian Mechanics uses canonical coordinates. Additionally, Lagrangian Mechanics is based on the principle of least action, while Hamiltonian Mechanics is based on the principle of stationary action.
Hamiltonian and Lagrangian Mechanics are used in a wide range of fields, including classical mechanics, quantum mechanics, and fluid dynamics. They are also used in engineering and physics to model and analyze the behavior of complex systems.
Hamiltonian Mechanics is a more general formulation of Lagrangian Mechanics, as it includes additional information about the system's energy. In some cases, the equations of motion derived from Hamiltonian and Lagrangian Mechanics can be equivalent.
One of the main advantages of using Hamiltonian and Lagrangian Mechanics is that they provide a more intuitive and elegant way to describe the dynamics of a system compared to traditional Newtonian mechanics. They also allow for more efficient and systematic calculations, making them useful for complex systems.
While Hamiltonian and Lagrangian Mechanics are powerful tools, they have some limitations. They are not applicable to all physical systems, such as non-conservative systems. They also require a high level of mathematical understanding and skill to use effectively.