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Lagrangian    
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  • 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
  • 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 The Hamiltonian runs over the time axis (the vertical axis in the drawing) while the Lagrangian runs over the trajectory of the moving particle, the t’-axis
  • The origin of the Lagrangian - Physics Stack Exchange
    Lagrangian mechanics uses the energy equation (1) to find the trajectory with the property that the rate of change of kinetic energy matches the rate of change of potential energy
  • What makes a Lagrangian a Lagrangian? - Physics Stack Exchange
    The Lagrangian is one implementation of an underlying geometry, called a "symplectic" geometry that connects kinematic variables with their conjugate dynamic variables, in the description of dynamics and laws of motion
  • Why are $L_4$ and $L_5$ lagrangian points stable?
    The "energy" (potential discussed above + kinetic energy measured in our non-inertial reference system) is conserved, because the Coriolis force is perpendicular to the trajectory, so it doesn't perform work (in fact, in Lagrangian mechanics it is derived from a potential that depends on the position and speed of the particle)
  • newtonian mechanics - Motivation for form $L = T - V$ of Lagrangian . . .
    Summarizing, Lagrangian, Newtonian and Hamiltonian mechanics are different mathematical frameworks whose goal is to describe the same physics The postulates of classical mechanics hold for all formalism, because they are facts of Nature, and we can use them to realize the passage from one to another scheme Of course, one must treat mathematical objects with care in order to gain the equivalence
  • Connection between different kinds of Lagrangian
    The third definition is different Of course it is also related in the sense that in Lagrangian formulations of dynamics or variational problems, Lagrange multiplier methods often appear But this third definition of a Lagrangian gets its name because of Lagrange multipliers, rather than because they are in any ways related to Lagrangians of variational problems I am not the best person to
  • Physical meaning of the Lagrangian function [duplicate]
    The point was, I wanted to have a physical interpretation of the Lagrangian, and leave the action and the principle as abstract constructions done for who knows what reason, probably because the principle is equivalent to the EL equations
  • lagrangian formalism - The proof of conservation of momentum in . . .
    In reading the first chapter of Mechanics by Landau and Lifshitz, there is one point on which I consistently get stuck This regards the proof in $\\S 7$ that space homogeneity implies conservatio
  • Why the Principle of Least Action? - Physics Stack Exchange
    And the Lagrangian is the answer to that, although it's not a 100% satisfactory one because the path that is taken need not strictly speaking be the truly least action path We integrate it, it gives us a kind of "cost", so to speak, which is then (partially) optimized and that gives us the "right" path of motion that an object "really" takes





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