Related papers: Exploring the long-term dynamics of perturbed Kepl…
We present several closed-form expressions of useful mass distributions. These include the potentials and accelerations of circular rings and arcs, the potentials of uniform density rings and arcs at arbitrary eccentricities, and the…
A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a…
A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
The rapid increase in the deployment of Low Earth Orbit (LEO) satellites, catering to diverse applications such as communication, Earth observation, environmental monitoring, and scientific research, has significantly amplified the…
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…
The perturbations of the hyperbolic motion of a test particle due to the general relativistic gravitoelectromagnetic Schwarzschild and Lense-Thirring components of the gravitational field of a rotating massive body are analytically worked…
A mathematical model is given for the occurrence of preferred orbits and orbital velocities in a Keplerian system. The result can be extended into energies and other properties of physical systems. The values given by the model fit closely…
Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…
Parabolic flights provide cost-effective, time-limited access to "weightless" or reduced gravity conditions experienced in space or on planetary surfaces, e.g. the Moon or Mars. These flights facilitate fundamental research - from materials…
Motion planning for articulated robots has traditionally been governed by algorithms that operate within manufacturer-defined payload limits. Our empirical analysis of the Franka Emika Panda robot demonstrates that this approach…
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…
Robotic assistance in scientific laboratories requires procedurally correct long-horizon manipulation, reliable execution under limited supervision, and robustness in low-demonstration regimes. Such conditions greatly challenge end-to-end…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
We present the Polar framework for fully automating the analysis of classical and probabilistic loops using algebraic reasoning. The central theme in Polar comes with handling algebraic recurrences that precisely capture the loop semantics.…
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $\Lambda$. It is shown that according to the current accuracy of satellite measurements…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying…