Related papers: An implicit symplectic solver for high-precision l…
Symplectic integrators are the preferred method of solving conservative $N$-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital…
The simulation of multi-body systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make the…
Contact-implicit motion planning-embedding contact sequencing as implicit complementarity constraints-holds the promise of leveraging continuous optimization to discover new contact patterns online. Nevertheless, the resulting optimization,…
The formation and evolution of protoplanetary systems, the breeding grounds of planet formation, is a complex dynamical problem that involves many orders of magnitudes. To serve this purpose, we present a new hybrid algorithm that combines…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time…
We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
The polysymplectic analysis of the Short Pulse Equation known in nonlinear optics is used in order to construct a geometric polysymplectic integrator for it. The proposed scheme turns out to be much more effective than other standard…
We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This…
We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gau\ss-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can…
Symplectic integrators with long-term preservation of integrals of motion are introduced for the guiding-center model of plasma particles in toroidal magnetic fields of general topology. An efficient transformation to canonical coordinates…
Due to the chaotic nature of the Solar System, the question of its dynamic long-term stability can only be answered in a statistical sense, e.g. based on numerical ensemble integrations of nearby orbits. Destabilization, including…
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7,…
We consider the numerical integration of the matrix Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, the Hill's equations originate from a Hamiltonian…
We present a detailed comparison of several integration schemes applied to the dynamic system consisting of a charged particle on the Kerr background endowed with the axisymmetric electromagnetic test field. In particular, we compare the…
Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…
An accurate and efficient method dealing with the few-body dynamics is important for simulating collisional N-body systems like star clusters and to follow the formation and evolution of compact binaries. We describe such a method which…
We present new almost time-reversible integrators for solution of planetary systems consisting of "planets" and a dominant mass ("star"). The algorithms can be considered adaptive generalizations of the Wisdom--Holman method, in which all…