A direct <i>N</i>-body integrator for modelling the chaotic, tidal dynamics of multibody extrasolar systems: <tt>TIDYMESS</tt>

A Linear-Time Variational Integrator for Multibody Systems

We present an efficient variational integrator for simulating multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equation, transforming forward integration into a root-finding problem for the DEL equation. Variational integrators have been shown to be more robust and accurate in preserving fundamental properties ...

The Comparison of Direct and Indirect Optimization Techniques in Equilibrium Analysis of Multibody Dynamic Systems

The present paper describes a set of procedures for the solution of nonlinear static-equilibrium problems in the complex multibody mechanical systems. To find the equilibrium position of the system, five optimization techniques are used to minimize the total potential energy of the system. Comparisons are made between these techniques. A computer program is developed to evaluate the equality co...

Dynamics of Multibody Systems

JANUS: A bit-wise reversible integrator for N-body dynamics

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the new N-body integrator JANUS, for which we achieve exact time-reversal symmetry by combining integer and floating point arithmetic. JANUS is explicit, formall...

Tidal Heating of Extrasolar Planets

Extrasolar planets close to their host stars have likely undergone significant tidal evolution since the time of their formation. Tides probably dominated their orbital evolution once the dust and gas cleared away, and as the orbits evolved there was substantial tidal heating within the planets. The tidal heating history of each planet may have contributed significantly to the thermal budget go...