相关论文: Five-body choreography on the algebraic lemniscate…

In his fondamental "Essay on the 3-body problem", Lagrange, well before Jacobi's "reduction of the node", carries out the first complete reduction of symetries. Discovering the so-called homographic motions, he shows that they necessarily…

The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…

An algorithm is presented for numerical computation of choreographies in spaces of constant negative curvature in a hyperbolic cotangent potential, extending the ideas given in a companion paper for computing choreographies in the plane in…

Gauss and Abel proved that the points dividing the unit circle and the lemniscate of Bernoulli in parts of equal length have algebraic coordinates. In this note we generalise these results to the Erd\H{o}s lemniscate with three leaves. We…

A pair of planar polygons is "dancing" if one is inscribed in the other and they satisfy a certain cross-ratio relation at each vertex of the circumscribing polygon. Non-degenerate dancing pairs of closed $n$-gons exist for all $n\geq 6$.…

We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual…

Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinations of past and future final motions. In particular, we…

Recently, it has been suggested that the Many-Body Localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert space preserving renormalization scheme that iteratively finds such integrals of motion…

The Dancing problem requires a swarm of $n$ autonomous mobile robots to form a sequence of patterns, aka perform a choreography. Existing work has proven that some crucial restrictions on choreographies and initial configurations (e.g., on…

In this paper, we consider minimizing the action functional as a method for numerically discovering periodic solutions to the $n$-body problem. With this method, we can find a large number of choreographies and other more general solutions.…

We present the results of a numerical search for periodic orbits with zero angular momentum in the Newtonian planar three-body problem with equal masses focused on a narrow search window bracketing the figure-eight initial conditions. We…

The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and…

Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants…

In this paper, we study the equations of motion for non-Abelian N=(2,0) tensor multiplets in six dimensions, which were recently proposed by Lambert and Papageorgakis. Some equations are regarded as constraint equations. We employ a loop…

The grand-canonical potential of many-body physics can be considered as a functional of the interaction-free correlation function. As such it obeys a nonlinear functional differential equation which can be turned into a recursion relation.…

The class of solvable many-body problems "of goldfish type" is extended by including (the additional presence of) three-body forces. The solvable $N$-body problems thereby identified are characterized by Newtonian equations of motion…

The wave is considered a paradigm in dance and connects bodily expression with nature. Although wave concepts such as propagation and phase have proven to be powerful tools for dance analysis, many aspects of bodily expression, including…

There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…

Over the years, several Bridges papers have delved into the concept of danceability of a knot diagram. Inspired by dancing on non-orientable surfaces, in this paper, we expand danceability to twisted virtual knot diagrams. This paper is…

We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…