相关论文: Alice and the Foucault Pendulum: the land of actio…

Lagrangian mechanics uses d'Alembert's principle of zero virtual work as an important starting point. The orthogonality of the force of constraint and virtual displacement is emphasized in literature, without a clear warning that this is…

The normal and the inverted pendulum continue to be one of the main physical models and metaphors in science. The inverted pendulum is also a classic study case in control theory. In this paper we consider a special demonstration version of…

A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be…

The detected anomalous frequency drift acceleration in Pioneer's radar data finds its explanation in a Berry phase that obtains the quantum state of a photon that propagates within an expanding space-time. The clock acceleration is just the…

We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…

Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems --…

- We have suggested using the action-angle variables for the study of a (quasi)particle in quantum ring. We have presented the action-angle variables for three two-dimensional singular oscillator systems - We have suggested a procedure of…

In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for…

The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle…

I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…

The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. In this paper we show that one can introduce a concept of angles to the fuzzy disc,…

This work shows that, Newton's Proposition 1 in the {\it Principia}, is an {\it exact} graphical representation of a canonical transformation, a first-order symplectic integrator generated at a finite time-step by the Hamiltonian. A…

A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of $n$ rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by…

We consider a quantum mechanical system to model the effect of quantum fields on the evolution of the early universe. The system consists of an inverted oscillator bilinearly coupled to a set of harmonic oscillators. We point out that the…

Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…

Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…

The traditional method of teaching canonical transformations involves the introduction of generating functions of various types. This method obscures the underlying structure of the Hamiltonian least-action principle, and can make a…

The present paper is a companion to the paper by Villone and Rampf (2017), titled "Hermann Hankel's On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861" together with…

We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…

The inverted pendulum is a mechanical system with a rapidly oscillating pivot point. Using techniques similar in spirit to the methodology of effective field theories, we derive an effective Lagrangian that allows for the systematic…