In this paper, structure-preserving time-integrators for rigid body-type mechanical systems
are derived from a discrete Hamilton–Pontryagin variational principle. From this principle …

This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian
systems on manifolds, akin to the Ornstein–Uhlenbeck theory of Brownian motion in a force …

Multibody systems are dynamical systems characterized by intrinsic symmetries and
invariants. Geometric mechanics deals with the mathematical modeling of such systems and …

We develop a framework for polynomial regression on Riemannian manifolds. Unlike
recently developed spline models on Riemannian manifolds, Riemannian polynomials offer …

This study derives geometric, variational discretization of continuum theories arising in fluid
dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central …

Casimir preserving integrators for stochastic Lie–Poisson equations with Stratonovich noise
are developed, extending Runge–Kutta Munthe-Kaas methods. The underlying Lie–Poisson …

We show that the motion of rigid bodies under water can be realistically simulated by
replacing the usual inertia tensor and scalar mass by the so-called Kirchhoff tensor. This …

In this contribution, we develop a variational integrator for the simulation of (stochastic and
multiscale) electric circuits. When considering the dynamics of an electric circuit, one is …

This paper demonstrates that the conditions for the existence of a dissipation-induced
heteroclinic orbit between the inverted and noninverted states of a tippe top are determined …

We investigate symmetry reduction of optimal control problems for left-invariant control affine
systems on Lie groups, with partial symmetry breaking cost functions. Our approach …