Variational formulation of linear time-dependent invariants

v 1 1 9 A pr 1 99 4 VARIATIONAL FORMULATION OF LINEAR TIME - DEPENDENT INVARIANTS ∗

It is shown that linear time-dependent invariants for arbitrary multi-dimensional quadratic systems can be obtained from the Lagrangian and Hamil-tonian formulation procedures by considering a variation of coordinates and mo-menta that follows the classical trajectory and defines a noetherian symmetry transformation.

Linear Time-dependent Invariants for Scalar Fields and Noether’s Theorem

The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether’s theorem procedure. PACS number(s): 03.65.Fd, 11.10.Ef.

On Some Applications of Time-dependent Invariants to the Semiclassical Formulation of Quantum Mechanics

I t i s shown, that time-dependent c lass ica l and quantum mechanical invariants (TDI) may be of considerable value in semiclassical formulations of time-dependent quantum mechanical problems. We demonstrate, that the application of TDI allows the application of several ground-state technologies as for instance the Wigner-Kirkwood and WKB-expansion to the TD s i tua t ion . Possible applicatio...

Delay-Dependent Robust Asymptotically Stable for Linear Time Variant Systems

In this paper, the problem of delay dependent robust asymptotically stable for uncertain linear time-variant system with multiple delays is investigated. A new delay-dependent stability sufficient condition is given by using the Lyapunov method, linear matrix inequality (LMI), parameterized first-order model transformation technique and transformation of the interval uncertainty in to the norm ...

Variational Formulation of Problems and Variational Methods