Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For a given analytic function $H$ from $\mathbb{C}$ to $\mathbb{C}$, we define the Polya Vector Field to be $\bar{H}$. This then corresponds to a irrotational, conservative vector field on $\mathbb{C}$.

Therefore in theory if we put a particle in a vector field $\bar{H}$ we should be able to solve for it's trajectory by $\ddot{z(t)}=\bar{H}$. So for $H=-1/z$ (which is like a negative point charge at the origin) I want to solve $\ddot{z(t)}=1/\bar{z}$. I haven't had any luck so far; the conjugate is throwing me off. I tried separating the real and imaginary parts but I am struggling to decouple these two odes. Any help appreciated.

However my main question is, is there anyway to solve $$\ddot{z(t)}=\bar{H}$$ generally?

share|improve this question

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.