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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 many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to… (More)

- Jerrold E. Marsden, Lawrence Sirovich, +5 authors Lawrence Perko
- 2010

We study Euler–Poincaré systems (i.e., the Lagrangian analogue of LiePoisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincaré equations for a parameter dependent Lagrangian by using a variational principle of Lagrange d’Alembert type. Then we derive an abstract Kelvin-Noether theorem for these… (More)

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 geometric structures as well as their preservation along solutions can be obtained directly from the variational principle. In particular, we prove that a unique… (More)

- Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
- IEEE Trans. Automat. Contr.
- 2000

We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler–Lagrange equations derived from the controlled Lagrangian describe the… (More)

- Anthony M. Bloch, Dong Eui Chang, Naomi Ehrich Leonard, Jerrold E. Marsden
- IEEE Trans. Automat. Contr.
- 2001

We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the… (More)

- Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden, Shane D. Ross
- Chaos
- 2000

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the… (More)

- Sanjay Lall, Jerrold E. Marsden, Sonja Glava
- 1999

In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems results in the usual balanced truncation. For nonlinear systems, the method makes used of the Karhunen-Loève decomposition of the state-space, and is an extension… (More)

- Razvan C. Fetecau, Jerrold E. Marsden, Michael Ortiz, Matthew West
- SIAM J. Applied Dynamical Systems
- 2003

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, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics… (More)

- Jerrold E. Marsden, C. TllUESDELL, Exterior Alsebra

Offprint/rom "A.rchive/or Rational Mechtmics tmd Analysis".