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 geometricâ€¦ (More)

Stability of relative equilibria for Hamiltonian systems is generally equated with Liapunov stability of the corresponding fixed point of the flow on the reduced phase space. Under mild assumptions,â€¦ (More)

A relative equilibrium of a Hamiltonian system with symmetry is a point of phase space giving an evolution which is a one-parameter orbit of the action of the symmetry group of the system. Theâ€¦ (More)

An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1:1 resonates with a frequency of the relativeâ€¦ (More)

Let P be a symplectic manifold with a free symplectic action of a connected compact Lie groupG. We show that, given a certain transversality condition, the set of relative equilibria E nearpe âˆˆ E ofâ€¦ (More)

Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. Theâ€¦ (More)

Due to a singularity or degeneracy at zero time-step, existence and uniqueness, and accuracy, of variational integrators, cannot be established by straightforward use of the implicit functionâ€¦ (More)

The geometry of constrained Lagrangian systems is developed using the Lagrange-d'Alembert principle, extending the variational approach of Marsden, Patrick and Shkoller [26] from holonomic toâ€¦ (More)

The retrograde fluorescent labeling technique reveals that trigeminal projections to the ventroposteromedial nucleus of the thalamus (VPM) of the rat originate from the main sensory nucleus (MSN) ofâ€¦ (More)

In the formalism of constrained mechanics, such as that which underlies the SHAKE and RATTLE methods of molecular dynamics, we present an algorithm to convert any one-step integration method to aâ€¦ (More)