24,672 research outputs found
Matching in the method of controlled Lagrangians and IDA-passivity based control
This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The -method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.\u
Euler-Lagrange correspondence of generalized Burgers cellular automaton
Recently, we have proposed a {\em Euler-Lagrange transformation} for cellular
automata(CA) by developing new transformation formulas. Applying this method to
the Burgers CA(BCA), we have succeeded in obtaining the Lagrange representation
of the BCA. In this paper, we apply this method to multi-value generalized
Burgers CA(GBCA) which include the Fukui-Ishibashi model and the quick-start
model associated with traffic flow. As a result, we have succeeded in
clarifying the Euler-Lagrange correspondence of these models. It turns out,
moreover that the GBCA can naturally be considered as a simple model of a
multi-lane traffic flow.Comment: 11 pages, 6 figures; accepted for publication in Int. J. Mod. Phys.
Contact variational integrators
We present geometric numerical integrators for contact flows that stem from a
discretization of Herglotz' variational principle. First we show that the
resulting discrete map is a contact transformation and that any contact map can
be derived from a variational principle. Then we discuss the backward error
analysis of our variational integrators, including the construction of a
modified Lagrangian. Throughout the paper we use the damped harmonic oscillator
as a benchmark example to compare our integrators to their symplectic
analogues
Remarks on Geometric Mechanics
This paper gives a few new developments in mechanics, as well as some remarks of a historical nature. To keep the discussion focused, most of the paper is confined to equations of "rigid body", or "hydrodynamic" type on Lie algebras or their duals. In particular, we will develop the variational structure of these equations and will relate it to the standard variational principle of Hamilton
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