# Double pendulum velocity derivation

1. Oct 2, 2010

### TheFerruccio

I'm doing a personal project and I'm refreshing my knowledge on Lagrangian mechanics. Right now, I am looking at the double pendulum example. How is the velocity of the 2nd mass derived, in terms of the angles of the two rods? 2nd mass as in, the mass that hangs lowest.

I have not been able to figure out the procedure to doing a derivation. The first mass velocity is relatively straightforward.

2. Oct 2, 2010

### TheFerruccio

I should probably give examples:

I got $$v_1^2$$ rather easily:

$$v_1^2 = l_1^2\dot\theta_1^2$$

But, v2 is expressed as:

$$v_2^2 = l_1^2\dot\theta_1^2+l_2^2\dot\theta_2^2+2l_1l_2\dot\theta_1\dot\theta_2\cos{(\theta_1-\theta_2)}$$