  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).
