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sams
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Is there any proof for the Lagrangian:
$$L = T - U $$
And why L = T - U ?
Any help is much appreciated. Thank you.
$$L = T - U $$
And why L = T - U ?
Any help is much appreciated. Thank you.
Is there any physical explanation why L = T - U? Why we have the negative sign in the Lagrangian equation in U?Orodruin said:What do you mean by proof? Lagrangian mechanics is a physics theory just as Newtonian mechanics. You don’t prove it, you test it experimentally.
sams said:Why we have the negative sign in the Lagrangian equation in U?
sams said:Is there any physical explanation why L = T - U? Why we have the negative sign in the Lagrangian equation in U?
This follows from the 2nd Newton Law +hypothesis that the constraints are ideal and holonomic +hypothesis that the forces are potentialsams said:Is there any proof for the Lagrangian:
$$L = T - U $$
And why L = T - U ?
Any help is much appreciated. Thank you.
The Lagrangian is a mathematical function used in classical mechanics to describe the dynamics of a system. It takes into account the kinetic and potential energies of the system and is used to derive the equations of motion.
The Lagrangian and Hamiltonian are two different ways to describe the same physical system. The Lagrangian is a function of the system's position and velocity, while the Hamiltonian is a function of the system's position and momentum.
The Lagrangian is a fundamental concept in classical mechanics and is used to describe the motion of particles and systems. It allows for a concise and elegant formulation of the equations of motion and has applications in fields such as astrophysics, engineering, and quantum mechanics.
In quantum field theory, the Lagrangian is used to describe the dynamics of particles and fields. It is a key component in the formulation of the Standard Model of particle physics and is used to calculate the probability amplitudes for interactions between particles.
Yes, the Lagrangian has applications in various areas of science, including economics, biology, and chemistry. It can be used to model and analyze complex systems and is a powerful tool for understanding the behavior of physical and mathematical systems.