Interest in Areas of Classical Mechanics

In summary, Hamiltonian/Lagrangian Mechanics are alternative formulations of classical mechanics that can be derived from Newtonian mechanics. They offer advantages in solving certain problems and provide a smoother transition to quantum mechanics. These concepts are typically taught in the third or fourth year of university, after a first-year course on Newtonian mechanics and with prerequisites in calculus and possibly differential equations. Popular textbooks include Fowles/Cassiday, Thornton/Marion, and Symon.
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Sho Kano
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What are Hamiltonian/Lagrangian Mechanics and how are they different from Newtonian?
What are the benefits to studying them and at what year do they generally teach you this at a university?
What are the maths required for learning them?
 
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Newtonian mechanics is based directly on Newton's laws of motion. Lagrangian and Hamiltonian mechanics are alternative formulations which can be derived from Newtonian mechanics. It's easier to solve certain types of problems using them. They also provide a more "natural" or "direct" transition to quantum mechanics.

In the USA, students usually study them in an "upper division" mechanics course in the third or fourth year of university (sometimes second year), following a first-year introductory physics course based on Newtonian mechanics. Prerequisites are at least a full calculus sequence including partial derivatives, probably also a course in differential equations, depending on how the mechanics course is taught. Typical textbooks are Fowles/Cassiday, Thornton/Marion, and Symon.

https://en.wikipedia.org/wiki/Lagrangian_mechanics
https://en.wikipedia.org/wiki/Hamiltonian_mechanics
 
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Related to Interest in Areas of Classical Mechanics

1. What is classical mechanics?

Classical mechanics is a branch of physics that deals with the motion of macroscopic objects and the forces acting on them. It is based on Newton's laws of motion and can be applied to a wide range of phenomena, from the motion of planets to the behavior of everyday objects.

2. Why is classical mechanics still important in modern science?

Classical mechanics is still relevant and widely used in modern science because it provides a fundamental understanding of how objects behave and interact with each other. It serves as the basis for more advanced branches of physics, such as quantum mechanics and relativity.

3. What are some practical applications of classical mechanics?

Classical mechanics has many practical applications in everyday life, such as designing machines and structures, predicting the motion of objects in sports and games, and understanding the behavior of fluids and gases. It also plays a crucial role in fields like engineering, astronomy, and navigation.

4. What are some key principles of classical mechanics?

Some key principles of classical mechanics include Newton's laws of motion, conservation of energy and momentum, and the principle of least action. These principles help to explain and predict the behavior of objects in motion.

5. How does classical mechanics differ from other branches of physics?

Classical mechanics differs from other branches of physics, such as quantum mechanics and relativity, in that it applies to macroscopic objects and is based on classical laws and principles. It also does not incorporate concepts like particle-wave duality and time dilation, which are central to other branches of physics.

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