It has been too long since I last computed rotational energy, but
I, moment of inertia, in the pendulum case, I = m * L^2, see, http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html
omega, angular velocity, d_theta / dt, which is theta dot.
Therefore K = 1/2 * I * omega^2 = 1/2 * m * L^2 * (theta dot)^2
Just to be sure, g in this case is denoting an acceleration? I think in the previous example g was denoting a force.
Yeah I believe g here is acceleration.
Usually, g stands for the acceleration of gravity, like weight = mass * gravity.
This MIT lecture on Engineering Dynamics helped me to understand this: https://www.youtube.com/watch?v=zhk9xLjrmi4
Mainly definition of Lagrangian at 1:45 and the example at 25:45.
It has been too long since I last computed rotational energy, but
I, moment of inertia, in the pendulum case, I = m * L^2, see, http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html
omega, angular velocity, d_theta / dt, which is theta dot.
Therefore K = 1/2 * I * omega^2 = 1/2 * m * L^2 * (theta dot)^2
Just to be sure, g in this case is denoting an acceleration? I think in the previous example g was denoting a force.
Yeah I believe g here is acceleration.
Usually, g stands for the acceleration of gravity, like weight = mass * gravity.
This MIT lecture on Engineering Dynamics helped me to understand this: https://www.youtube.com/watch?v=zhk9xLjrmi4
Mainly definition of Lagrangian at 1:45 and the example at 25:45.