- #1
RickRazor
- 17
- 3
In the paper http://physics.unipune.ernet.in/~phyed/26.2/File5.pdf, the author solves the LC-circuit using Euler-Lagrange equation. She assumes that the Lagrangian function for the circuit is $$L=T-V$$ where
$$T=L\dot q^2/2$$ is the kinetic energy part $$V=q^2 / 2C$$ is the potential energy.She then goes on to say that $$
\frac{d}{dt} \left ( \frac{\partial L}{\partial \dot q} \right ) - \frac{\partial L}{\partial q} = 0
$$
is the equation of motion. I have a couple of questions:1) Is Hamilton's principle applicable here? If yes, why is the kinetic energy $$
\dfrac{{L\dot q^2}}{2}
?$$
2) Inductors also store potential energy temporarily in the magnetic field. Why don't we consider that term?
$$T=L\dot q^2/2$$ is the kinetic energy part $$V=q^2 / 2C$$ is the potential energy.She then goes on to say that $$
\frac{d}{dt} \left ( \frac{\partial L}{\partial \dot q} \right ) - \frac{\partial L}{\partial q} = 0
$$
is the equation of motion. I have a couple of questions:1) Is Hamilton's principle applicable here? If yes, why is the kinetic energy $$
\dfrac{{L\dot q^2}}{2}
?$$
2) Inductors also store potential energy temporarily in the magnetic field. Why don't we consider that term?