Redundant configuration coordinates and nonholonomic velocity coordinates in analytical mechanics

Analytical Mechanics of Chemical Reactions . III . Natural Collision Coordinates *

The analytical mechanics (quantum and classical) of chemically reactive linear collisions were treated in earlier papers of this series.1•2 The main features of the treatment were (1) a set of coordinates which passed smoothly from those suited to reactants, through those suited to "activated complexes," to those suited to products, (2) a zeroth-order solution which was "vibrationally adiabatic...

Statistical Mechanics in Collective Coordinates

We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Si...

Tensor Coordinates in Noncommutative Mechanics

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly used, and the object of noncommutativity θ plays a fundamental rule as an independent quantity. The presented classical theory, as its quantum counterpart, is ...

Geometry optimization in redundant internal coordinates

The gradient geometry-optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual NewtonRaphson-type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage s...

Maximum-entropy meshfree coordinates in computational mechanics