What is the difference between Newtonian and Lagrangian mechanics in a . . . Lagrangian mechanics are better when there are lots of constraints The more the constraints, the simpler the Lagrangian equations, but the more complex the Newtonian become Lagrangian mechanics is not very suited for non-ideal or non-holonomic systems, such as systems with friction Lagrangian mechanics is also much more extensible
How is Lagrangian Mechanics useful? - Physics Stack Exchange Also can Lagrangian be used to solve any of the problems out there in mechanics easily? very much so Go to the problems section of your textbook on the Lagrangian Mechanics chapter, find a problem near the back of the section, and try to solve it using a Newtonian approach It will quickly become clear just how useful the Lagrangian approach is
The origin of the Lagrangian - Physics Stack Exchange To explain the form of the Lagrangian the energy equation is essential The animation below consists of 7 frames, each frame is displayed for 3 seconds In the upper-left sub-panel of the combined diagram the black line represents a trial trajectory The animation sweeps through a range of trajectory variation In the upper right sub-panel:
What is the physical meaning of the action in Lagrangian mechanics? The Hamiltonian H and Lagrangian L which are rather abstract constructions in classical mechanics get a very simple interpretation in relativistic quantum mechanics Both are proportional to the number of phase changes per unit of time
Momentum in Lagrangian mechanics - Physics Stack Exchange Lagrangian mechanics, though, is much more general as pointed out by the other answers It allows one to study other systems with other generalized momentum associated with translational invariance Share
lagrangian formalism - The proof of conservation of momentum in . . . The underlying solid point is that if the Lagrangian does not change value on shifting the system in space (or shifting values of the coordinates), then value of $\sum_a \frac{\partial L}{\partial \mathbf v_a}$ is conserved
lagrangian formalism - Whats the point of Hamiltonian mechanics . . . First of all, Lagrangian is a mathematical quantity which has no physical meaning but Hamiltonian is physical (for example, it is total energy of the system, in some case) and all quantities in Hamiltonian mechanics has physical meanings which makes easier to have physical intuition
Interpretations of Lagrangian vs. Hamiltonian mechanics In Lagrangian mechanics, you have the principle of least action, generalized coordinates, manifest Lorentz invariance (for relativistic theories), Noether's theorem So the two formalisms are useful for different things and certain concepts are easier to express in one vs another
general relativity - Whats the Lagrangian density means? - Physics . . . The Lagrangian density measures the "distribution of the Lagrangian over space" For General Relativity, there is no obvious way (lacking some symmetry) in which one should split space-time up into space and time, and so it becomes natural to use the Lagrangian density and integrate over all of spacetime rather than trying to figure out how one