Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one–dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of partial derivatives in the Schrödinger operator. PACS-numbers: 0320 (Classical mechanics of discrete systems; general mathematical aspects); 0365 (Quantum mech...

Two linear algebra based strategies are presented to deal with general classical mechanics problems with constraints. Classical concepts such as holonomic and nonholonomic constraints, virtual displacements, principle of virtual work, Hamilton’s principle and method of Lagrange multipliers are critiqued.

An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to describe of the nonpotential interaction of a systems. The procedure of splitting of a system into equilibrium subsystems, presentation of subsystem’s energy ...

We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a related paper, we show that the time evolution of a set of quantum initial data satisfying these criteria is fully consistent with the predictions of a new theory...

In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance a model is understood as its under action matrix Lie group transformations parametrized by arbitrary functions. It formally presented property introduced in such systems, followed modern applications. Furthermore, Lagrangians describing systems are s...

In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, [1]. I treat some classical systems with various potentials and some Physical interpretations are given concerning the presence of noncommutativity at large scales (Celeste Mechanics) directly tied to the one present at small scales (Quant...