Moment of inertia of a double physical pendulum

[AF Fardin]

Homework Statement

My task is to solve the equation of motion for a double "physical" pendulum!

Relevant Equations

L=T-V
$\tau=Fr=I\alpha

I am having trouble to find the moment of inertia of the second rod!
Is it related to the first rod??
At the beginning I thought It's not!
But when took those as constant,the equation had become way much simpler and there is nothing about chaos!
My approach is given below

 

[TSny]

Use the fact that the kinetic energy of either rod is the sum of two contributions:

(1) the kinetic energy due to the motion of the center of mass of the rod: $\frac {1}{2} M V_{cm}^2$

(2) the kinetic energy due to rotation about the center of mass: $\frac{1}{2} I_{cm} \omega^2$

 

[PeterDonis]

Homework Statement:: My task is to solve the equation of motion for a double "physical" pendulum!
Relevant Equations:: L=T-V
$\tau=Fr=I\alpha

My approach is given below

Equations in images are not allowed; please use the PF LaTeX support to enter equations directly into your post. There is a "LaTeX Guide" link at the bottom left of the post window.

 

[PeterDonis]

Moderator's note: Thread moved to advanced physics homework help.

 

[Orodruin]

The big problem here is the assumption that
$$
T = \frac 12 (I_1\dot\theta_1^2 + I_2\dot\theta_2^2)
$$
The kinetic energy cannot be written on this form. Note that the second rod will also move when $\theta_1$ changes.

Note: The angles are the angles each rod make with the vertical. This does not mean that the motion of rod 2 is independent of $\theta_1$.
I made an exam problem with different coordinates for a double pendulum… that really threw some people off …