Palindrom said:Under what conditions can I "build" a Hamiltonian from a given Lagrangian?
I'm thinking it might have something to do with the potential, but it's not really clear to me what it is the question is.
I think that might be it. Besides, they gave me the kinetical energy, but not the potential, so it's probably it.dextercioby said:Any conditions,provided the Lagrangian has the "familiar" form:Kinetic-Potential energy.
It has no connection with the potential,as long it is coordinate dependent only and does not contain "generalized velocities".
Daniel
PS.In the first statement i included the degenerate systems.
Classical mechanics is a branch of physics that deals with the motion of objects and the forces that cause them to move. It is important because it provides a fundamental understanding of the physical world and is the basis for many other areas of physics, such as thermodynamics, electromagnetism, and quantum mechanics.
The main principles of classical mechanics are Newton's laws of motion, which state that an object will remain at rest or in uniform motion unless acted upon by an external force, and that the force acting on an object is equal to its mass times its acceleration. Other important principles include conservation of energy and momentum, and the principle of least action.
Classical mechanics has many practical applications, including designing structures and machines, predicting the motion of objects in space, and understanding the behavior of fluids. It is also crucial for fields such as engineering, architecture, and astronomy.
Classical mechanics describes the behavior of macroscopic objects, while quantum mechanics deals with the behavior of subatomic particles. Classical mechanics is deterministic, meaning that the future state of a system can be predicted based on its current state, while quantum mechanics is probabilistic and involves uncertainty in predicting the behavior of particles.
One common misconception is that classical mechanics is only applicable to large-scale objects. In reality, it can also accurately describe the behavior of smaller objects, as long as they are not at the quantum scale. Another misconception is that classical mechanics is outdated and has been replaced by modern physics, when in fact it is still widely used and relevant in many areas of science and engineering.