576 citations · 1.9k across the 50 of their papers we have counts for
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Covariant Balance Laws in Continua with Microstructure
Arash Yavari, Jerrold E. Marsden
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transforma…
The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices
Joris Vankerschaver, Eva Kanso, Jerrold E. Marsden
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating…
Discrete Mechanics and Optimal Control: an Analysis
S. Ober-Bloebaum, O. Junge, J. E. Marsden
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal ene…
A resolution of the transition to turbulence paradox
Rouslan Krechetnikov, Jerrold E. Marsden
Understanding the transition to turbulence has been impeded by a modeling oversight
On the stability analysis in the transition to turbulence problem
R. Krechetnikov, J. E. Marsden
In this note, which is of general stability theory interest, we discuss some of the key assertions usually stated in the context of the transition to turbulence problem. In particu…
Variational Integrators for Maxwell's Equations with Sources
Ari Stern, Yiying Tong, Mathieu Desbrun +1
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by…
Hamilton-Pontryagin Integrators on Lie Groups: Introduction and Structure-Preserving Properties
Nawaf Bou-Rabee, Jerrold E. Marsden
In this paper structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton-Pontryagin variational principle. From this principl…