Canonical transformation

About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.

The Inverse Monodromy Transform is a Canonical Transformation

Abstract: Publisher Summary This chapter discusses the inverse monodromy transform, explaining how it is a canonical transformation. The Inverse Monodromy Transform (IMT) parallels the Inverse Scattering Transform (IST). The finite dimensional solution manifold for these flows is not necessarily compact, not a torus, and so the KAM theorem does not directly apply. The potential connection between a possible preservation of the solution manifold and the preservation of the Painleve property is an intriguing one. Now the contours are the same as those used in the integral definitions of Airy functions.

Symplectic phase flow approximation for the numerical integration of canonical systems

Abstract: New methods are presented for the numerical integration of ordinary differential equations of the important family of Hamiltonian dynamical systems. These methods preserve the Poincare invariants and, therefore, mimic relevant qualitative properties of the exact solutions. The methods are based on a Runge-Kutta-type ansatz for the generating function to realize the integration steps by canonical transformations. A fourth-order method is given and its implementation is discussed. Numerical results are presented for the Henon-Heiles system, which describes the motion of a star in an axisymmetric galaxy.

Canonical transform for tracking with kinematic models

Abstract: A canonical transform is presented that converts a coupled or uncoupled kinematic model for target tracking into a decoupled dimensionless canonical form. The coupling is due to non-zero off-diagonal terms in the covariance matrices of the process noise and/or the measurement noise, which can be used to model the coupling of motion and/or measurement between coordinates. The decoupled dimensionless canonical form is obtained by simultaneously diagonalizing the noise covariance matrices, followed by a spatial-temporal normalization procedure. This canonical form is independent of the physical specifications of an actual system. Each subsystem corresponding to a canonical coordinate is characterized by its process noise standard deviation, called the maneuver index as a generalization of the tracking index for target tracking, which characterizes completely the performance of a steady-state Kalman filter. A number of applications of this canonical form are discussed. The usefulness of the canonical transform is illustrated via an example of performance analysis of maneuvering target tracking in an air traffic control (ATC) system.