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We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
We analyse the potential of the electric solar wind sail for solar system space missions. Applications studied include fly-by missions to terrestrial planets (Venus, Mars and Phobos, Mercury) and asteroids, missions based on non-Keplerian…
The Lagrange point $L_1$ for the Sun-Earth system is considered due to its special importance for the scientific community for the design of space missions. The location of the Lagrangian points with the trajectories and stability regions…
We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a…
We consider the Kepler problem on surfaces of revolution that are homeomorphic to $S^2$ and have constant Gaussian curvature. We show that the system is maximally superintegrable, finding constants of motion that generalize the Runge-Lentz…
Understanding solar turbulent convection and its influence on differential rotation has been a challenge over the past two decades. Current models often overestimate giant convection cells amplitude, leading to an effective Rossby number…
Saturn's moon Enceladus is an exciting destination for future exploration missions due to the scientifically interesting geyser region located on its South pole. In this work, we compile the different types of science orbit configurations…
We study the two-dimensional motion of a self-propelling asymmetric bent rod. By employing slender body theory and the Lorentz reciprocal theorem, we determine particle trajectories for different geometric configurations and arbitrary…
This study proposes a new automated strategy for designing and optimizing three-dimensional interplanetary low-thrust (LT) trajectories. The method formulates the design as a hybrid optimal control problem and solves it using a two-step…
The latest high-performance telescopes for deep space observation employ very large primary mirrors that are made of smaller segments, like the JWST which employs monolithic beryllium hexagonal segments. A very promising development stage…
For a solar-like star, the surface rotation evolves with time, allowing in principle to estimate the age of a star from its surface rotation period. Here we are interested in measuring surface rotation periods of solar-like stars observed…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
A small variation of the circular shape of the hodograph theorem states that for every elliptical solution of the two-body problem, it is possible to find an appropriate inertial frame such that the speed of the bodies is constant. We use…
The solar gravitational lens (SGL) offers unique capabilities for high-resolution imaging of faint, distant objects, such as exoplanets. In the near future, a spacecraft carrying a meter-class telescope with a solar coronagraph would be…
We consider the Klein-Gordon equation on a Riemannian surface which is globally well-posed in the energy space. This equation has an homoclinic orbit to the origin, and in this paper we study the dynamics close to it. Using a strategy from…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
The logarithmic potential is of great interest and relevance in the study of the dynamics of galaxies. Some small corrections to the work of Contopoulos & Seimenis (1990) who used the method of Prendergast (1982) to find periodic orbits and…
In this note, we prove that below the first critical energy level, a proper combination of the Ligon-Schaaf and Levi-Civita regularization mappings provides a convex symplectic embedding of the energy surfaces of the planar rotating Kepler…
This paper discusses the geometry of a surface endowed with a slope metric. We obtain necessary and sufficient conditions for any surface of revolution to admit a strongly convex slope metric. Such conditions involve certain inequalities…
This paper considers the motion control of a particle and a spinning disc on rotating earth. The equations of motion are derived using Lagrangian mechanics. Trajectory planning is studied as an optimization problem using the method referred…