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Hi everyone

At first I want to find the langrangian function and the equation of motion for a system which exists of 2 masses(m) coupled by a spring(k). It's moving in 3 dimensions.We shall use cylindrical coordinates

Langrangian

At first I tried to find the kinetic energy

[tex] T= \frac 1 2 m(\dot r_{1}^{2}+r_{1}^{2} \dot \phi_{1}^{2}+\dot z_{1}^{2})+\frac 1 2 m(\dot r_{2}^{2}+r_{2}^{2} \dot \phi_{2}^{2}+\dot z_{2}^{2})[/tex]

Is that right or did I do any mistakes thus far?

Now I tried to find the potential energy. I found the absolute value of the vector r1-r2

but I'm not sure if that's right because it looks 'too complicated'. I thought there's a trick to simplify it.

The absolute value of a vector for r1-r2 I found is:

[tex]r_{1}^{2}+r_{2}^{2}-2r_{1}r_{2}(cos_{1}(\phi)cos_{2}(\phi)+sin_{1}( \phi)sin_{2}(\phi))+z_{1}^{2}-2z_{1}z_{2}+z_{2}^{2}[/tex]

square root of this, but for the potential energie ^2 so I just left the square root out.

Can anyone confirm this? Or did I do any mistakes there? Thanks for your help in advance

/edit: or would it be more intelligent to use the center of mass of the system as the point of origin ?

## Homework Statement

At first I want to find the langrangian function and the equation of motion for a system which exists of 2 masses(m) coupled by a spring(k). It's moving in 3 dimensions.We shall use cylindrical coordinates

## Homework Equations

Langrangian

## The Attempt at a Solution

At first I tried to find the kinetic energy

[tex] T= \frac 1 2 m(\dot r_{1}^{2}+r_{1}^{2} \dot \phi_{1}^{2}+\dot z_{1}^{2})+\frac 1 2 m(\dot r_{2}^{2}+r_{2}^{2} \dot \phi_{2}^{2}+\dot z_{2}^{2})[/tex]

Is that right or did I do any mistakes thus far?

Now I tried to find the potential energy. I found the absolute value of the vector r1-r2

but I'm not sure if that's right because it looks 'too complicated'. I thought there's a trick to simplify it.

The absolute value of a vector for r1-r2 I found is:

[tex]r_{1}^{2}+r_{2}^{2}-2r_{1}r_{2}(cos_{1}(\phi)cos_{2}(\phi)+sin_{1}( \phi)sin_{2}(\phi))+z_{1}^{2}-2z_{1}z_{2}+z_{2}^{2}[/tex]

square root of this, but for the potential energie ^2 so I just left the square root out.

Can anyone confirm this? Or did I do any mistakes there? Thanks for your help in advance

/edit: or would it be more intelligent to use the center of mass of the system as the point of origin ?

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