Friday, June 28, 2013

1306.6448 (Dario Izzo et al.)

Solution of the constant radial acceleration problem using Weierstrass
elliptic and related functions

Dario Izzo, Francesco Biscani
We consider the constant radial acceleration problem. While the problem is known to be integrable and has received some recent attention in an orbital mechanics context, a closed form explicit solution, relating the state variables to an anomaly, has eluded all researchers so far. We show how such a solution exists and is elegantly expressed in terms of the Weierstrass elliptic and related functions $\wp$,$\zeta$ and $\sigma$. We show how previously known facts can be derived from the new explicit solution and discuss new insights such an approach reveal.
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