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The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization-invariant theories.

Muslih, S.I. (2002)

International Journal of Mathematics and Mathematical Sciences

The equivalence of controlled lagrangian and controlled hamiltonian systems

Dong Eui Chang, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden, Craig A. Woolsey (2002)

ESAIM: Control, Optimisation and Calculus of Variations

The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...

The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems

Dong Eui Chang, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden, Craig A. Woolsey (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...

The first Birkhoff coefficient and the stability of 2-periodic orbits on billiards.

Kamphorst, Sylvie Oliffson, Pinto-de-Carvalho, Sônia (2005)

Experimental Mathematics

The $ℤ$ -graded symplectic Floer cohomology of monotone Lagrangian submanifolds.

Li, Weiping (2004)

Algebraic & Geometric Topology

The hamiltonian formalism in higher order variational problems

Mauro Francaviglia, Demeter Krupka (1982)

Annales de l'I.H.P. Physique théorique

The Helmholtz conditions for the difference equations systems.

Crăciun, Dumitru, Opriş, Dumitru (1996)

Balkan Journal of Geometry and its Applications (BJGA)

The $n$ -centre problem of celestial mechanics for large energies

Andreas Knauf (2002)

Journal of the European Mathematical Society

We consider the classical three-dimensional motion in a potential which is the sum of $n$ attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the $n$ centres, we find a universal behaviour for all energies $E$ above a positive threshold. Whereas for $n = 1$ there are no bounded orbits, and for $n = 2$ there is just one closed orbit, for $n \geq 3$ the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set....

The shadowing chain lemma for singular Hamiltonian systems involving strong forces

Marek Izydorek, Joanna Janczewska (2012)

Open Mathematics

We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.

The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics

V. Jurdjevic (2009)

Annales de l'I.H.P. Analyse non linéaire

Currently displaying 1 – 13 of 13