Solved 2 1 A Firm Has Production Function Q 3ké Lá Chegg In the context of translation symmetry for lagrangian mechanics i was given this statement: for a mechanical system $\frac {∂l} {∂\dot {q} i}=p i$ is the momentum. i have no idea where this comes from. The lagrangian formulation can get complicated with non conservative systems and more generally forces that are not obtained by the gradient of a potential the generalized forces must be added by hand and in these situations the lagrangian approach is clearly a variation on the newtonian approach.
Solved 2 1 A Firm Has Production Function Q 3ké Lá Chegg 66 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. 5 as was said in the commentary by @knzhou, what you have written is the lagrangian for a particle with magnetic moment and no charge (e.g. like neutron). then your logic is correct: as long as magnetic field is uniform, the particle will experience no force. 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. We vary the action is the density of lagrangian of the system. so, by integrating by parts we obtain: we have to determine the density of the lagrangian. one terms deals with the interaction of the charges with the electromagnetic field, . the other term is the density of energy of the electromagnetic field: this term is the difference of the magnetic field and the electric field. so we have.
Solved A Write Down The Lagrangian Function For The Chegg 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. We vary the action is the density of lagrangian of the system. so, by integrating by parts we obtain: we have to determine the density of the lagrangian. one terms deals with the interaction of the charges with the electromagnetic field, . the other term is the density of energy of the electromagnetic field: this term is the difference of the magnetic field and the electric field. so we have. 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. So seeing an equivalence between the hamiltonian for qed and the covariant form of the lagrangian for qed would involve some additional steps to handle those gauge constraint ambiguities. but i'm assuming you aren't interested in those details for this question. 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. 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.
Solved 4 Cost Minimization Problem Using A Lagrangian Chegg 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. So seeing an equivalence between the hamiltonian for qed and the covariant form of the lagrangian for qed would involve some additional steps to handle those gauge constraint ambiguities. but i'm assuming you aren't interested in those details for this question. 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. 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.
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