Related papers: Collision trajectories and regularisation of two-b…
The two full body problem concerns the dynamics of two spatially extended rigid bodies (e.g. rocky asteroids) subject to mutual gravitational interaction. In this note we deduce the Euler-Poincare and Hamiltonian equations of motion using…
This work introduces a novel path-following control strategy inspired by the famous two-body problem, aiming to stabilize any Keplerian orbit. Utilizing insights from the mathematical structure of the two-body problem, we derive a robust…
We prove the existence of chaotic trajectories for the two body problem on a sphere. The trajectories we construct encounter near-collisions and are similar to the second species solutions of Poincar\'e of the classical 3 body problem. The…
We consider the two-body problem on surfaces of constant non-zero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show there are two relative equilibria where the masses are…
We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier-Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
Consider the dynamics of two point masses on a surface of constant curvature subject to an attractive force analogue of Newton's inverse square law. When the distance between the bodies is sufficiently small, the reduced equations of motion…
The central collision between two solid spheres or the normal collision between a sphere and a plate are important to understand in detail before studying more complex particle interactions. Models exist to describe this basic problem but…
This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is…
We report in experiment and simulation the spontaneous formation of dynamically bound pairs of shape changing robots undergoing locally repulsive collisions. These physical `gliders' robustly emerge from an ensemble of individually…
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a-posteriori framework for computer assisted existence proofs. Our framework is applied to the…
A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, Plakhov & Gouveia…
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between…
Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the…
We study the isosceles three-body problem with Manev interaction. Using a McGehee-type technique, we blow up the triple collision singularity into an invariant manifold, called the collision manifold, pasted into the phase space for all…
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by…