Open AccessThe Lagrangian and Hamiltonian for RLC Circuit: Simple Case
Author(s) -
Albertus Hariwangsa Panuluh
Publication year - 2020
Publication title -
international journal of applied sciences and smart technologies
Language(s) - English
Resource type - Journals
eISSN - 2685-9432
pISSN - 2655-8564
DOI - 10.24071/ijasst.v2i2.2519
Subject(s) - rlc circuit , hamiltonian (control theory) , hamiltonian mechanics , legendre transformation , classical mechanics , physics , hamiltonian system , lagrangian , inductance , covariant hamiltonian field theory , mathematics , mathematical analysis , quantum mechanics , capacitor , voltage , mathematical optimization , phase space
The Lagrangian and Hamiltonian for series RLC circuit has been formulated. We use the analogical concept of classical mechanics with electrical quantity. The analogy is as follow mass, position, spring constant, velocity, and damping constant corresponding with inductance, charge, the reciprocal of capacitance, electric current, and resistance respectively. We find the Lagrangian for the LC, RL, RC, and RLC circuit by using the analogy and find the kinetic and potential energy. First, we formulate the Lagrangian of the system. Second, we construct the Hamiltonian of the system by using the Legendre transformation of the Lagrangian. The results indicate that the Hamiltonian is the total energy of the system which means the equation of constraints is time independent. In addition, the Hamiltonian of overdamping and critical damping oscillation is distinguished by a certain factor.