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Hi

Look at the drawing. Furthermore I have a constant acceleration [tex] \vec g = -g \hat y[/tex]

I shall find the Lagrange function and find the equation of motion afterwards.

Lagrange/ Euler function and eqauation

I found out the following for the kinetic energy and the potential energy:

[tex] T=\frac {1} {2} m_{1} \dot{\vec r_{1}}^{2} + \frac {1} {2} m_{2} \dot{\vec r_{2}}^{2}[/tex]

and for the potential energy:

[tex] V=\frac 1 2 k_{1}{\vec r_{1}}^{2}+\frac 1 2 k_{2} {\vec r_{2}}^{2}+m_{1}gy_{1}+m_{2}gy_{2}+\frac 1 2 k_{3}({\vec r_{1}}-{\vec r_{2}})^{2}[/tex]

Now I used the Euler- Lagrange equation of motion and found out that:

[tex] m_{1}\ddot{\vec r_{1}}=-k_{1}{\vec r_{1}}+k_{3}{\vec r_{1}}-m_{1}g\hat y[/tex]

and

[tex] m_{2}\ddot{\vec r_{2}}=-k_{2}{\vec r_{2}}-k_{3}{\vec r_{2}}-m_{2}g\hat y [/tex]

Can anyone confirm this? Or did I do any mistakes?

Thanks for your help

## Homework Statement

Look at the drawing. Furthermore I have a constant acceleration [tex] \vec g = -g \hat y[/tex]

I shall find the Lagrange function and find the equation of motion afterwards.

## Homework Equations

Lagrange/ Euler function and eqauation

## The Attempt at a Solution

I found out the following for the kinetic energy and the potential energy:

[tex] T=\frac {1} {2} m_{1} \dot{\vec r_{1}}^{2} + \frac {1} {2} m_{2} \dot{\vec r_{2}}^{2}[/tex]

and for the potential energy:

[tex] V=\frac 1 2 k_{1}{\vec r_{1}}^{2}+\frac 1 2 k_{2} {\vec r_{2}}^{2}+m_{1}gy_{1}+m_{2}gy_{2}+\frac 1 2 k_{3}({\vec r_{1}}-{\vec r_{2}})^{2}[/tex]

Now I used the Euler- Lagrange equation of motion and found out that:

[tex] m_{1}\ddot{\vec r_{1}}=-k_{1}{\vec r_{1}}+k_{3}{\vec r_{1}}-m_{1}g\hat y[/tex]

and

[tex] m_{2}\ddot{\vec r_{2}}=-k_{2}{\vec r_{2}}-k_{3}{\vec r_{2}}-m_{2}g\hat y [/tex]

Can anyone confirm this? Or did I do any mistakes?

Thanks for your help