On the stability of a space vehicle riding on an intense laser beam
  The Breakthrough Starshot Initiative is suggested to develop the concept of propelling a nano-scale spacecraft by the radiation pressure of an intense laser beam. If such a nanocraft could be accelerated to 20 percent of light speed, it could reach the vicinity of our nearest potentially habitable exoplanet within our life time and capture its images and obtain other scientific data. In this project the nanocraft is a gram-scale robotic spacecraft comprising two main parts: StarChip and Lightsail.   To achieve the goal of the project it is necessary to solve a number of outstanding scientific problems. One of these tasks is to make sure that the nanocraft position and orientation inside the intense laser beam column is stable. The nanocraft driven by intense laser beam pressure acting on its Lightsail is sensitive to the torques and lateral forces reacting on the surface of the sail. These forces influence the orientation and lateral displacement of the spacecraft, thus affecting its dynamics. If unstable the nanocraft might be expelled from the area of laser beam. In choosing the models for nanocraft stability studies we are using several assumptions: 1. configuration of nanocraft is treated as rigid body (applicability of Euler equations); 2. flat or concave shape of circular sail; 3. mirror reflection of laser beam from surface of the Lightsail. We found conditions of position stability for spherical and conical shape of the sail. The simplest stable configurations require the StarChip to be removed from the sail to make the distance to the center of mass of nanocraft bigger than curvature radius of the sail. Stability criteria do not require the spinning of the nanocraft. A flat sail is never stable (even with spinning). 
H. Popova and M. Efendiev and I. Gabitov
astro-ph.IM