 #1
 219
 0
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
Attachments

7.2 KB Views: 393