We illustrate the theory of one-dimensional pluri-Lagrangian systems with the example of commuting billiard maps in confocal quadrics.

In the present paper nonholonomic systems with drift terms are studied. The discussion is focused on a class of Lagrangian systems with a cyclic coordinate. We present an approach to open-loop path planning in which the system evolution is studied on manifolds of dimension equal to the number of control inputs. A control procedure is derived and it is applied to the planar diver. 1999 Elsevier ...

The aim of this paper is to provide a geometric description and classification of general systems of ordinary differential equations of order s ≥ 1 on fibered manifolds, and to investigate geometric properties of solutions of these equations. The present setting covers Lagrangian systems, higher order semisprays, and constrained systems (equations subject to constraints modeled by exterior diff...

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 modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In th...

This paper proposes a new approach based on augmented Lagrangian relaxation for short term generation scheduling problem with transmission and environmental constraints. In this method, the system constraints, e.g. load demand, spinning reserve, transmission capacity and environmental constraints, are relaxed by using Lagrangian multipliers, and quadratic penalty terms associated with system lo...

We first review the nonrelativistic lagrangian theory as a framework for the MOND equation. Obstructions to a relativistic version of it are discussed leading up to TeVeS, a relativistic tensor-vectorscalar field theory which displays both MOND and Newtonian limits. The whys for its particular structure are discussed and its achievements so far are summarized.

This motivates the following definition. Definition 1.2. A conserved quantity in a Hamiltonian system is a smooth function f ∈ C∞(M) such that {f,H} = 0. Remark 1.3. If you’re familiar with the Lagrangian model of classical mechanics, you can derive the above setup from a Lagrangian field theory on the real line R, i.e. from classical Lagrangian mechanics. There’s a classical procedure for doin...

This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inpu...