What was the intuition behind the development of Hamiltonian mechanics?

In summary, the conversation discusses the relationship between Hamiltonian mechanics and Newtonian mechanics, and whether Hamiltonian mechanics is a mathematical generalization or explains a fundamental relationship with nature. The speaker also asks about the influence of William Rowan Hamilton and the role of Langrangian mechanics.
  • #1
omie
4
2
Is Hamiltonian mechanics a mathematical generalization of Newtonian mechanics or is it explaining some fundamental relationship that has a meaning that extends into our nature ? I guess my question is what would led William Rowan Hamilton to come up with his type of mechanics or anything relating to that.
 
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  • #2
omie said:
Is Hamiltonian mechanics a mathematical generalization of Newtonian mechanics
Yes
or is it explaining some fundamental relationship that has a meaning that extends into our nature ?
What is "extending into our nature" in the framework of physics? Isn't all physics describing nature?
I guess my question is what would led William Rowan Hamilton to come up with his type of mechanics or anything relating to that.
I absolutely can't speak for him. Historians may do a better job. What is about Langrangian mechanics? Do you think it is sort of step between?
 

Related to What was the intuition behind the development of Hamiltonian mechanics?

1. What is Hamiltonian mechanics?

Hamiltonian mechanics is a mathematical framework for describing the motion of particles or systems of particles. It was developed by William Rowan Hamilton in the 19th century as an alternative to Newtonian mechanics.

2. What was the motivation behind the development of Hamiltonian mechanics?

The main motivation behind the development of Hamiltonian mechanics was to find a more elegant and general formulation of classical mechanics. Hamilton was dissatisfied with the limitations of Newtonian mechanics and sought to develop a more comprehensive theory.

3. What is the role of the Hamiltonian in this theory?

The Hamiltonian is a function that describes the total energy of a system in terms of its position and momentum. It plays a central role in Hamiltonian mechanics, as it allows for the prediction of future states of a system based on its current state.

4. How does Hamiltonian mechanics differ from other formulations of classical mechanics?

Unlike Newtonian mechanics, which is based on the concept of forces, Hamiltonian mechanics is based on the concept of energy. This allows for a more elegant and general formulation, as it can be applied to a wider range of physical systems.

5. What are the practical applications of Hamiltonian mechanics?

Hamiltonian mechanics has many practical applications in physics, engineering, and other fields. It is used to describe the motion of particles in fields such as quantum mechanics, fluid dynamics, and celestial mechanics. It also has applications in control theory and optimization problems.

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