@article{Bassetto2022, 
author = {Marco Bassetto and Alessandro A. Quarta and Giovanni Mengali},
title = {Analytical solution to logarithmic spiral trajectories with circumferential thrust and mission applications},
year = {2022},
journal = {Astrodynamics},
volume = {6},
number = {4},
pages = {413-427},
keywords = {circumferential thrust, logarithmic spiral trajectory, circle-to-circle transfer},
url = {https://www.sciopen.com/article/10.1007/s42064-022-0135-3},
doi = {10.1007/s42064-022-0135-3},
abstract = {This study made use of a shape-based method to analyze the orbital dynamics of a spacecraft subject to a continuous propulsive acceleration acting along the circumferential direction. Under the assumption of a logarithmic spiral trajectory, an exact solution to the equations of motion exists, which allows the spacecraft state variables and flight time to be expressed as a function of the angular coordinate. There is also a case characterized by specific initial conditions in which the time evolution of the state variables may be analytically determined. In this context, the presented solution is used to analyze circle-to-circle trajectories, where the combination of two impulsive maneuvers and a logarithmic spiral path are used to accomplish the transfer. The determined results are then applied to the achievement of the Earth–Mars and the Earth–Venus transfers using actual data from a recent thruster developed by NASA.}
}