I may have forgotten basic derivatives, but why do we know again that the time derivative of dl/dtheta_dot is mL^2theta_doubledot?
triangle
So we are taking the derivative of L, and the only parts with theta_dot is the first term so we are taking the derivative of .5mL^2theta_dot^2. By the power rule, the 2 in the exponent comes down and cancels out the .5 coefficient.
bepis
@sponge So you first take the derivative of dL/dtheta_dot, which is just taking the derivative of m1/2L^2*theta_dot^2 since this is the only term with theta_dot. You treat everything not theta_dot as a constant and get mL^2theta_dot. Theta dot is already the first order time derivative of theta (dot is just notation for the first order derivative, and double dot is notation for second order derivative) so taking the derivative wrt time again will make it the second order time derivative, which is theta double dot. Theta_dot is the only term that involves time, so we can leave the mL^2 term as is.
I may have forgotten basic derivatives, but why do we know again that the time derivative of dl/dtheta_dot is mL^2theta_doubledot?
So we are taking the derivative of L, and the only parts with theta_dot is the first term so we are taking the derivative of .5mL^2theta_dot^2. By the power rule, the 2 in the exponent comes down and cancels out the .5 coefficient.
@sponge So you first take the derivative of dL/dtheta_dot, which is just taking the derivative of m1/2L^2*theta_dot^2 since this is the only term with theta_dot. You treat everything not theta_dot as a constant and get mL^2theta_dot. Theta dot is already the first order time derivative of theta (dot is just notation for the first order derivative, and double dot is notation for second order derivative) so taking the derivative wrt time again will make it the second order time derivative, which is theta double dot. Theta_dot is the only term that involves time, so we can leave the mL^2 term as is.
Yep! This all sounds right to me.