3 research outputs found
Tidal interactions of a Maclaurin spheroid. II: Resonant excitation of modes by a close, misaligned orbit
We model a tidally forced star or giant planet as a Maclaurin spheroid,
decomposing the motion into the normal modes found by Bryan (1889). We first
describe the general prescription for this decomposition and the computation of
the tidal power. Although this formalism is very general, forcing due to a
companion on a misaligned, circular orbit is used to illustrate the theory. The
tidal power is plotted for a variety of orbital radii, misalignment angles, and
spheroid rotation rates. Our calculations are carried out including all modes
of degree , and the same degree of gravitational forcing. Remarkably,
we find that for close orbits () and rotational deformations
that are typical of giant planets () the component of the
gravitational potential may significantly enhance the dissipation through
resonance with surface gravity modes. There are also a large number of
resonances with inertial modes, with the tidal power being locally enhanced by
up to three orders of magnitude. For very close orbits (), the
contribution to the power from the modes is roughly the same magnitude as
that due to the modes.Comment: 14 pages, 9 figures, accepted for publication in MNRA
C-Learning: Horizon-Aware Cumulative Accessibility Estimation
Multi-goal reaching is an important problem in reinforcement learning needed
to achieve algorithmic generalization. Despite recent advances in this field,
current algorithms suffer from three major challenges: high sample complexity,
learning only a single way of reaching the goals, and difficulties in solving
complex motion planning tasks. In order to address these limitations, we
introduce the concept of cumulative accessibility functions, which measure the
reachability of a goal from a given state within a specified horizon. We show
that these functions obey a recurrence relation, which enables learning from
offline interactions. We also prove that optimal cumulative accessibility
functions are monotonic in the planning horizon. Additionally, our method can
trade off speed and reliability in goal-reaching by suggesting multiple paths
to a single goal depending on the provided horizon. We evaluate our approach on
a set of multi-goal discrete and continuous control tasks. We show that our
method outperforms state-of-the-art goal-reaching algorithms in success rate,
sample complexity, and path optimality. Our code is available at
https://github.com/layer6ai-labs/CAE, and additional visualizations can be
found at https://sites.google.com/view/learning-cae/.Comment: Accepted at ICLR 202