  Sparse trajectory data consist of a low number of trajectories such that the
reconstruction of an underlying velocity field is not possible. Recently,
approaches have been introduced to analyze flow behavior based on a single
trajectory only: trajectory stretching exponent (TSE) to detect hyperbolic
(stretching) behavior, and trajectory angular velocity (TRA) to detect elliptic
(rotation) behavior. In this paper, we analyze these approaches and in
particular show that they are -- contrary to what is claimed in the literature
-- not objective in the extended phase space. Furthermore, we introduce the
first objective measure of rotation behavior that is based on only few
trajectories: at least 3 in 2D, and at least 4 in 3D. For this measure --
called trajectory vorticity (TRV) -- we show that it is objective and that it
can be introduced in two independent ways: by approaches for unsteadiness
minimization and by considering the relative spin tensor. We apply TRV to a
number of constructed and real trajectory data sets, including drifting buoys
in the Atlantic, midge swarm tracking data, and a simulated vortex street.
