On the origin and nature of finite-amplitude instabilities in physical systems (2009)
Krechetnikov, R., Marsden, J. E.
Finite-amplitude instabilities are ubiquitous, but their theory and precise definitions require clarification. In this work, we discuss the interrelation of various notions connected with...
A low-dimensional model of separation bubbles (2009)
Krechetnikov, R., Marsden, J. E., Nagib, H. M.
In this work, motivated by the problem of model-based predictive control of separated flows, we identify the key variables and the requirements on a model-based observer and construct a prototype...
A low-dimensional model of separation bubbles (2009)
Krechetnikov, R., Marsden, J. E., Nagib, H. M.
In this work, motivated by the problem of model-based predictive control of separated flows, we identify the key variables and the requirements on a model-based observer and construct a prototype...
F. Gabern, W. S. Koon, J. E. Marsden
Abstract. We study a simple model for an asteroid pair, namely a planar system consisting of a rigid body and a sphere. This model is interesting because it is one of the simplest that captures the...
Arch. Rational Mech. Anal. (2003) Digital Object Identifier (DOI) 10.1007/s00205-002-0212-y (2009)
Asynchronous Variational Integrators, A. Lew, J. E. Marsden, M. Ortiz, M. West
We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of...
INTRODUCTION INVARIANT MANIFOLDS, THE SPATIAL THREE-BODY PROBLEM AND SPACE MISSION DESIGN (2009)
G. Gómez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont, S. D. Ross
C. Kane, J. E. Marsden, M. Ortiz
Time-discretized variational formulation of non-smooth frictional contact
Lagrangian Averaging for Compressible Fluids (2009)
H. S. Bhat, R. C. Fetecau, J. E. Marsden, K. Mohseni, M. West
Abstract. This paper extends the derivation of the Lagrangian averaged Euler (LAE-α) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the...
Dissipation-induced instabilities in finite dimensions Contents (2009)
R. Krechetnikov, J. E. Marsden
The goal of this work is to introduce a coherent theory of the counter-intuitive phenomena of dynamical destabilization under the action of dissipation. While the existence of one class of
2006 On destabilizing effects of two fundamental non-conservative forces (2008)
Physica D, R. Krechetnikov, J. E. Marsden
In this work we discuss the instabilities in mechanical systems caused by two fundamentally different non-conservative forces, referred to as dissipative and positional forces, each of which may lead...
CDS and Graduate Aeronautical Laboratories, Caltech (2008)
C. Kane, J. E. Marsden, M. Ortiz, Politecnico Di Milano, Edited B. Fiedler, K. Gröger, ...
This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the...
Lagrangian Averaging for Compressible Fluids (2008)
H. S. Bhat, R. C. Fetecau, J. E. Marsden, K. Mohseni, M. West
Abstract. This paper extends the derivation of the Lagrangian averaged Euler (LAE-α) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the...
Variational multisymplectic formulations of nonsmooth continuum mechanics (2008)
R. C. Fetecau, J. E. Marsden, M. West
To Larry Sirovich on the occasion of his 70th birthday ABSTRACT This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE...
Celestial Mech., 9:81–103, 1974. (2008)
J. E. Marsden, M. Mccracken, The Hopf Bifurcation, K. R. Meyer, M. Gutzwiller
[1] K. R. Meyer and D. S. Schmidt. Periodic orbits near L4 for mass ratios near the critical
Keywords: Stabilization of Non-linear Systems, Dissipative (2008)
C. A. Woolsey, A. M. Bloch, N. E. Leonard, J. E. Marsden
We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a...
LOW ENERGY TRANSFER TO THE MOON (2008)
W. S. Koon, M. W. Lo, J. E. Marsden, S. D. Ross
Abstract. In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less �V than a standard Hohmann transfer. In this paper, we apply the...
Variational time integrators (2008)
A. Lew, J. E. Marsden, M. Ortiz, M. West
The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the...
Systems and Control Letters 1(1981): 92-94. (2008)
J. E. Marsden, Foundations Of Mechanics, Second Edition, Benjamin Cummings, D. Z. Arov, M. G. Krein, ...
Schmidt pairs for a Hankel operator and the generalized Schur-Takagi
J. E. Marsden, T. S. Ratiu, S. Shkoller
This paper develops the geometric analysis of geodesic flow of a new right invariant metric 〈·, ·〉1 on two subgroups of the volume preserving diffeomorphism group of a smooth n-dimensional...
Binary Asteroid Observation Orbits from a Global Dynamical Perspective ∗ (2008)
F. Gabern, W. S. Koon, J. E. Marsden, D. J. Scheeres
Abstract. We study spacecraft motion near a binary asteroid by means of theoretical and computational tools from geometric mechanics and dynamical systems. We model the system assuming that one of...
G. G. Luther, G. G. Luther, M. S. Alber, M. S. Alber, J. E. Marsden, J. E. Marsden, ...
Frequency conversion and its control among three light waves is analyzed using a geometric approach that enables the dynamics of the waves to be visualised on a closed surface in three dimensions. It...
L. Kharevych, Weiwei Y. Tong, E. Kanso, J. E. Marsden, P. Schröder, M. Desbrun
We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physics-based animation techniques. Several...
G. G. Luther, M. S. Alber, J. E. Marsden, J. M. Robbins
Frequency conversion and its control among three light waves is analyzed using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It...
This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of...
Locomotion of articulated bodies in a perfect fluid (2005)
E. Kanso, J. E. Marsden, C. W. Rowley
Summary. This paper is concerned with modeling the dynamics of N articulated solid bodies submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals due to the...
New York, R. Abraham, J. E. Marsden, T. Ratiu Manifolds, Tensor Analysis, Milton Abramowitz, ...
[9] G. E. Albert. A general theory of stochastic estimates of the Neuma series for solution of
Mass-Related Dynamical Barriers in Triatomic Reactions (2005)
T. Yanao, W. S. Koon, J. E. Marsden
Abstract. A methodology is given to determine the effect of different mass distributions for triatomic reactions using the geometry of shape space. Atomic masses are incorporated into the...
M. Dellnitz, K. A. Grubits, J. E. Marsden, K. Padberg, B. Thiere
We present a new method based on set oriented computations for the calculation of reaction rates in chemical systems. The method is demonstrated with the Rydberg atom, an example for which...
Application of Tube Dynamics to Non-Statistical Reaction Processes (2005)
F. Gabern, W. S. Koon, J. E. Marsden, S. D. Ross, T. Yanao
Abstract. A technique based on dynamical systems theory is introduced for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that...
Connecting orbits and invariant manifolds in the spatial restricted three-body problem (2004)
G. Gomez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont, S. D. Ross
The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view....
Connecting orbits and invariant manifolds in the spatial restricted three-body problem (2004)
G. Gómez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont, S. D. Ross
The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometric point of view....
Nonsmooth Lagrangian mechanics and variational collision integrators (2003)
Fetecau, R. C., Marsden, J. E., Ortiz, M., West, M.
Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions,...
Design of a multi-moon orbiter (2003)
S. D. Ross, W. S. Koon, M. W. Lo, J. E. Marsden
The Multi-Moon Orbiter concept is introduced, wherein a single spacecraft orbits several moons of Jupiter, allowing long duration observations. The ∆V requirements for this mission can be low if...
Nonsmooth Lagrangian mechanics and variational collision integrators (2003)
R. C. Fetecau, J. E. Marsden, M. Ortiz, M. West
Abstract. Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for...
Dissipation and controlled Euler-Poincaré systems (2001)
C. A. Woolsey, A. M. Bloch, N. E. Leonard, J. E. Marsden
The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These...
2001], Resonance and capture of Jupiter comets (2001)
W. S. Koon, M. W. Lo, J. E. Marsden, S. D. Ross
Abstract. A number of Jupiter family comets such as Oterma and Gehrels 3 make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of...
References � Numerical Collision Papers (2000)
Jerry Marsden, Couro Kane, Michael Ortiz, Anna Pandolfiand, Matt West, E. A. Repetto, ...
• Problems and techniques are motivated by the study of systems in which complex collision sequences can occur. • Our integration methods are based on discretizations of variational principles...
G. G. Luther, M. S. Alber, J. E. Marsden, J. M. Robbins
INTRODUCTION Energy conversion among light waves occurs in optical materials where the interaction of the light with the material is well characterized by expansion of the polarizability up to at...
C. Kane, J. E. Marsden, M. Ortiz, M. West
The purpose of this work is twofold. First, we demonstrate analytically that the classical Newmark family as well as related integration algorithms are variational in the sense of the Veselov...
C. Kane, J. E. Marsden, M. Ortiz
The purpose of this work is twofold. First, we demonstrate analytically that the classical Newmark family as well as related integration algorithms are variational in the sense of the Veselov...
Finite element analysis of nonsmooth contact (1999)
C. Kane, C. Kane, E. A. Repetto, E. A. Repetto, M. Ortiz, M. Ortiz, ...
This work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem...
Finite Element Analysis of Nonsmooth Contact (1999)
C. Kane, E. A. Repetto, M. Ortiz, J. E. Marsden
This work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem...
Abstract Finite element analysis of nonsmooth contact (1998)
C. Kane, E. A. Repetto, M. Ortiz, J. E. Marsden
work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem is...
Symplectic-Energy-Momentum Preserving (1998)
Variational Integrators, C. Kane, J. E. Marsden, M. Ortiz
The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic, energy and momentum conserving. To do this, a spacetime view of variational...
Nonholonomic Mechanical Systems with Symmetry (1995)
Bloch, A. M., Krishnaprasad, P. S., Marsden, J. E., Murray, R. M.
This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control theoretical...
Dimensional Model Reduction in Non-linear Finite Element Dynamics of Solids and Structures
P. Krysl, S. Lall, J. E. Marsden
this paper given as wall-clock measurements on an 225 MHz SGI Octane workstation with R10K processor, 128 MB of memory, and 32 KB instruction and data caches, and 1 MB secondary cache. Copyright c