The three-dimensional Euler equations have stood for a quarter of a millenium as a
challenge to mathematicians and physicists. While much has been discovered, the nature of …

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a
stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to …

In this historical review we describe in detail the main stages of the development of
nonholonomic mechanics starting from the work of Earnshaw and Ferrers to the monograph …

A multisymplectic Lie algebra variational integrator (MLAVI) for simulating the dynamics of a
flexible multibody system is proposed. The flexible bodies are described by the …

Estimation of spacecraft mass properties in the presence of noise is a nontrivial problem
that, when properly addressed, can substantially reduce the crew time devoted to cargo …

A new variational principle for mechanical systems subject to holonomic constraints is
presented. The newly proposed GGL principle is closely related to the often used Gear …

Coordinate-free Lie-group integration method of arbitrary (and possibly higher) order of
accuracy for constrained multibody systems (MBS) is proposed in the paper. Mathematical …

Using discrete variational principle, a Hamel's field variational integrator (HFVI) for
simulating dynamics of thin-walled geometrically exact beams with war** effects is …

We describe discretisations of the shallow-water equations on the sphere using the
framework of finite element exterior calculus, which are extensions of the mimetic finite …

Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models,
we present a general framework for introducing stochasticity into variational principles …