Double Pendulum Problem - Lagrangian

[Nusc]

Homework Statement

Rather than solve the double pendulum problem with two masses in the usual way.

Instead express the coordinates of the second mass, in terms of the coordinates of the mass above it.

$$x2=x_1+\xi = L_1Sin[\theta]Cos[\phi]+L_2Sin[\alpha]Cos[\beta]\\<br /> y2=y_1+ \eta = L_1Sin[\theta]Sin[\phi]+L_2Sin[\alpha]Sin[\beta]\\<br /> z2=z_1-\xi = L_1-L_1Cos[\theta]-L_2Sin[\alpha]Cos[\beta]$$Wouldn't you suspect that the Lagrangian remain invariant? Is there a way to reparameterize these equations?

Homework Equations

The Attempt at a Solution

 

[Nusc]

No one has any opinions?

Does anyone know what I'm talking about?

 

[Nusc]

Then the problem I'm interested in is the following

 

[Nusc]

this is the spherical double pendulum involving lagrangian reduction.

http://www.springerlink.com/content/x726522458q205m7/


The mathematica picture above is incorrect.

 

[Nusc]

I'm not sure if I had defined z_2 correct:
$$<br /> <br /> z2=z_1-\xi = L_1-L_1Cos[\theta]-L_2Cos[\alpha]<br />$$