- #1
fluidistic
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I'm not sure where to post this question. In classical mechanics many problems are simplified in the approximation of "small angles" or "small oscillations".
Wikipedia gives the following criteria or approximations:
[itex]\sin \theta \approx \theta[/itex].
[itex]\cos \theta \approx 1 - \frac{\theta ^2}{2}[/itex]
[itex]\tan \theta \approx \theta[/itex].
But in some books I find the relation:
[itex]\cos \theta \approx 1[/itex].
In other words they discard any terms of second degree and higher, keeping terms of degree 0 and 1 only.
Now when I tackle a problem of small oscillations I do not know what criteria to use. Of course keeping terms of second order gives a more accurate result... but I am not sure this is the standard.
What is your experience with this?
Wikipedia gives the following criteria or approximations:
[itex]\sin \theta \approx \theta[/itex].
[itex]\cos \theta \approx 1 - \frac{\theta ^2}{2}[/itex]
[itex]\tan \theta \approx \theta[/itex].
But in some books I find the relation:
[itex]\cos \theta \approx 1[/itex].
In other words they discard any terms of second degree and higher, keeping terms of degree 0 and 1 only.
Now when I tackle a problem of small oscillations I do not know what criteria to use. Of course keeping terms of second order gives a more accurate result... but I am not sure this is the standard.
What is your experience with this?