Is Lagrangian mechanics used in engineering?

Yes lagrangians and hamiltonians are indeed used by engineers. To be precise, used by some types of engineers like aeronautical engineers, aerodynamics etc..

Are Hamiltonian mechanics useful?

Hamiltonian mechanics gives nice phase-space unified solutions for the equations of motion. And also gives you the possibility to get an associated operator, and a coordinate-independent sympletic-geometrical interpretation. The former is crucial in quantum mechanics, the later is crucial in dynamical systems.

What is the difference between Lagrangian and Hamiltonian?

Lagrangian mechanics can be defined as a reformulation of classical mechanics. The key difference between Lagrangian and Hamiltonian mechanics is that Lagrangian mechanics describe the difference between kinetic and potential energies, whereas Hamiltonian mechanics describe the sum of kinetic and potential energies.

How would you differentiate between the Lagrangian and the Hamiltonian formulations of mechanics?

The key difference between Lagrangian and Hamiltonian mechanics is that Lagrangian mechanics describe the difference between kinetic and potential energies, whereas Hamiltonian mechanics describe the sum of kinetic and potential energies.

Can Jack Fraser solve the JEE paper Quora?

Jack Fraser, a third year physics student at the University of Oxford was previously tagged on Quora and was asked to solve a JEE Question paper. Often deemed as the hardest exam, the paper was solved by Fraser “in like one-third of the allotted time and with 100\% correct answers”.

Why are there Lagrangian and Hamiltonian mechanics?

The Hamiltonian has twice as many independent variables as the Lagrangian which is a great advantage, not a disadvantage, since it broadens the realm of possible transformations that can be used to simplify the solutions. Hamiltonian mechanics uses the conjugate coordinates q,p, corresponding to phase space.

What are the two big formulations of classical mechanics?

As classical mechanics was formulated into more advanced and deeper forms of advanced mechanics expressing the laws of physics more and more fundamentally, two big formulations of classical mechanics were developed; Lagrangian mechanics and Hamiltonian mechanics.

What is the difference between Lagrangian mechanics and Hamiltonian mechanics?

This you can read more about in my introductory article on special relativity. One of the key differences that becomes explicitly important in for example quantum mechanics, is the fact that Hamiltonian mechanics uses position and momentum to describe motion and Lagrangian mechanics mainly deals with position and velocity.

What is the best book for learning Lagrangian mechanics?

My personal favorite self-study book for this is No-Nonsense Classical Mechanics by Jakob Schwichtenberg (click to check price on Amazon), which is overall the best beginner-friendly resource on Lagrangians, Hamiltonians and advanced classical mechanics in general that I’ve found.

How are the equations of motion obtained in Lagrangian mechanics?

In Lagrangian mechanics, the equations of motion are obtained by something called the Euler-Lagrange equation, which has to do with how a quantity called action describes the trajectory (path in space) that a particle or a system will take. A detailed derivation and explanation of the Euler-Lagrange equation can be found in one of my articles here.