Double Pendulum Problem - Lagrangian

  • Thread starter Nusc
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  • #1
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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.

[tex]
$ x2=x_1+\xi = L_1Sin[\theta]Cos[\phi]+L_2Sin[\alpha]Cos[\beta]$\\
$ y2=y_1+ \eta = L_1Sin[\theta]Sin[\phi]+L_2Sin[\alpha]Sin[\beta]$\\
$ z2=z_1-\xi = L_1-L_1Cos[\theta]-L_2Sin[\alpha]Cos[\beta]$
[/tex]


Wouldn't you suspect that the Lagrangian remain invariant? Is there a way to reparameterize these equations?

Homework Equations





The Attempt at a Solution

 

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Answers and Replies

  • #2
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No one has any opinions?

Does anyone know what I'm talking about?
 

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Last edited:
  • #3
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Then the problem I'm interested in is the following
 

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  • #5
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I'm not sure if I had defined z_2 correct:
[tex]


$ z2=z_1-\xi = L_1-L_1Cos[\theta]-L_2Cos[\alpha]$

[/tex]
 

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