[PDF] Top 20 Controlled Lagrangian and Hamiltonian systems

... Next, we show that the method of controlled Lagrangian systems and its Hamiltonian counterpart, the method of controlled Hamiltonian systems, are equivalent for simple mechanical systems[r] ... See full document

... In this relation, we should mention the results of Hi- rota et al. [8], in which the authos carefully rearrange terms to figure out the definiteness of the second variation of the Hamiltonian was carried out. ... See full document

... The link between the treatment of singular Lagrangians as field systems and the canonical Hamiltonian approach is studied. It is shown that the singular Lagrangians as field sys- tems are always in exact ... See full document

... control systems, biological systems or chemical processes ...power systems, most generation units are interfaced to the grid via synchronous generators ... See full document

... variable systems to have a consistent approach to these ...the Lagrangian, Hamiltonian and a constant of motion of the gravitational attraction of two bodies were given when one of the bodies has ... See full document

... The need to exploit this simple observation was felt when dealing with initial-boundary value problems as opposed to initial-value problems. It was used to its full extent in the development of the so-called unified ... See full document

... a Lagrangian, and a Hamiltonian for the nonrelativistic ...the Lagrangian and Hamiltonian cannot be given expli- citly in ...the Lagrangian can be found explicitly, but the ... See full document

... both Lagrangian and Hamiltonian formalisms on ...dynamical systems (1)-(2) in the form of a unique Kähler dynamical system, together with its specific geometrical underpinning called the Kähler-Ricci ... See full document

... a Lagrangian submanifold L then lo c a lly , about L, there is a uniquely defined one form B sa tis fy in g ( i ) d0 = w ( i i ) i(X )0 = 0 fo r X lyin g in A and ( i i i ) 6 0 ... See full document

... the Lagrangian and Hamiltonian approaches for some non-dissipative and some dissipative systems have some problems ...different Hamiltonian to the same classical system [7], implying that one ... See full document

... [1] Hamiltonian systems described by linear, constant-coefficient ordinary differential equations (in the following ‘‘Hamiltonian 1D systems’’) were studied using the formalism of quadratic- ... See full document

... Controlled Lagrangian method is an energy shaping method designed to control underactuated mechanical ...the Controlled Lagrangian method to attain more freedom in controller parameters; ... See full document

... and Hamiltonian are of foundamental concepts in classical mechanics and there are many researches about ...of Lagrangian systems and constants of motion (conservsd quantity) are related to each ... See full document

... nonlinear systems via their approximate discrete-time model was presented in [4, ...dissipative systems and hence approximate discrete-time models can be obtained using various numerical algorithms, such as ... See full document

... regular Lagrangian) does in fact contain a closed, invertible 2-form—a symplectic structure, in seeming analogy with Hamiltonian mechanics—as part of the equation’s construction, as we intimated immediately ... See full document

... singular Lagrangian system can be transformed into phase space and described by Hamiltonian canonical variables; there are inherent constraints between canonical variables, namely constrained ... See full document

... This symmetry between x and t naturally suggests a notion of duality in the process of choos- ing x or t as the evolution parameter defining the integrable picture. Note also that the approach to discretization of ... See full document

... Recently, the Reidemeister torsion has found interesting applications in dynamical systems theory. A connection between the Lefschetz type dynamical zeta functions and the Reidemeister torsion was established by ... See full document

... grable systems have a number of interesting properties: they can be separable in more than one coordinate system; all bounded orbits are closed; they give rise to interesting Poisson algebras with polynomial ... See full document

... split-generates then K is not displaceable from any Lagrangian submanifold L with HF(L, L) 6 = 0 . Finding a split-generator is also the first step in many modern proofs of homological mirror symmetry (for example ... See full document