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Ayo everybody, I'm doing a problem about theory of small oscilatons (see pic) and I got the following for potential energy:

[itex] V= mg(\frac{l_{2}}{2} +\frac{l_{1}}{2} \theta^{2}_{1} + \frac{l_{2}}{4} \theta^{2}_{2}) [/itex] (after the aproximation [itex] cos \theta [/itex]~ [itex]1 - \frac{\theta^{2}}{2} [/itex]

Knowing that [itex] V = \frac{1}{2} V_{jk} \theta_{jk} [/itex] I need to write the matrix [itex] V_{jk}[/itex]

Since the term [itex] mg\frac{l_{2}}{2} [/itex] is constant, can I remove it from the potential ?

And write the matrix like this:

[itex] V_{jk} =mg \begin{pmatrix}

l_{1} & 0 \\

0 & \frac{l_{2}}{2} \\

\end{pmatrix}

[/itex]

If not, how can I remove the constant term?

[itex] V= mg(\frac{l_{2}}{2} +\frac{l_{1}}{2} \theta^{2}_{1} + \frac{l_{2}}{4} \theta^{2}_{2}) [/itex] (after the aproximation [itex] cos \theta [/itex]~ [itex]1 - \frac{\theta^{2}}{2} [/itex]

Knowing that [itex] V = \frac{1}{2} V_{jk} \theta_{jk} [/itex] I need to write the matrix [itex] V_{jk}[/itex]

Since the term [itex] mg\frac{l_{2}}{2} [/itex] is constant, can I remove it from the potential ?

And write the matrix like this:

[itex] V_{jk} =mg \begin{pmatrix}

l_{1} & 0 \\

0 & \frac{l_{2}}{2} \\

\end{pmatrix}

[/itex]

If not, how can I remove the constant term?

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