Related papers: Slimplectic Integrators: Variational Integrators f…
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to…
We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
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…
We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In…
Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, nonexistence of attractors, and good behaviour of statistical…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
We consider symplectic time integrators in numerical General Relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard…
This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent Hamiltonians. For the first time, explicit symplectic…
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…
Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences…
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…
We describe a method for symplectic tracking of charged particles through static electric and magnetic fields. The method can be applied to cases where the fields have a dependence on longitudinal as well as transverse position, and where…
We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral…