Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The equations of motions for the double pendulum is given by

$$\dot{\theta_1} = \frac{6}{ml^2}\frac{2p_{\theta1} - 3\cos(\theta_1 - \theta_2)p_{\theta2}}{16 - 9\cos^2(\theta_1 - \theta_2)}$$

and similarly for the other pendulum. In respect to what does the change in angle for the first pendulum refer to? Is it with respect to time? So that $\dot{\theta_1} = \frac{d\theta}{dt}$?

share|cite|improve this question

Yes. The point always refers to the derivative with respect to time.

share|cite|improve this answer

The dot over a function or variable Isaac Newton's notation for a derivative; in physics it always means a derivative with respect to time.

Variables with two or three dots, like $\ddot{\theta}$ and $\dddot{\theta}$, represent second and third time derivatives respectively.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.