Related papers: Brachistochrone Problem and Vaconomic Mechanics
Recently, the quantum brachistochrone problem is discussed in the literature by using non-Hermitian Hamilton operators of different type. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the…
We study some aspects of the Quantum Brachistochrone Problem. Physical realizability of the faster pseudo Hermitian version of the problem is also discussed. This analysis, applied to simple quantum gates, supports an informational…
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical…
Vakonomic mechanics has been proposed as a possible description of the dynamics of systems subject to nonholonomic constraints. The aim of the present work is to show that for an important physical system the motion brought about by…
We consider the problem of finding paths of shortest transit time between two points (popularly known as Brachistochrone) for cylinders with off-centered center of mass, rolling down without slip, subject solely to the force of gravity.…
If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by…
We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…
The main aim of the present paper is to raise the doubt that vakonomic dynamics may not be satisfactory as a model for velocity dependent constraints.
In this paper we develop a discussion about PT Symmetric Quantum Mechanics, working with basics elements of this theory. In a simple case of two body system, we developed the Quantum Brachistochrone problem. Comparing the results obtained…
We treat the vakonomic dynamics with general constraints within a new geometric framework which will be appropriate to study optimal control problems. We compare our formulation with Vershik-Gershkovich one in the case of linear…
We solve the brachistochrone problem for a particle travelling through a spherical mass distribution of uniform density. We examine the connection between this problem and the popular "gravity elevator" result. The solution is compared to…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
In this paper, variational techniques are used to analyze the dynamics of nonholonomic mechanical systems with impacts. Implicit nonholonomic smooth Lagrangian and Hamiltonian systems are extended to a nonsmooth context appropriate for…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called \v{C}aplygin systems.
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
The Brachistochrone problem, which describes the curve that carries a particle under gravity in a vertical plane from one height to another in the shortest time, is one of the most famous studies in classical physics. There is a similar…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…