Friday, June 28, 2013

1306.6448 (Dario Izzo et al.)

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

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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