• Support PF! Buy your school textbooks, materials and every day products Here!

Classical mechanics

  • Thread starter rmfw
  • Start date
53
0
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?
 

Attachments

Last edited:

Answers and Replies

33,579
9,315
Constant terms don't matter, you can ignore them. They just reflect the arbitrary choice of "zero height".
 

Related Threads for: Classical mechanics

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
10
Views
949
  • Last Post
Replies
6
Views
4K
Top