Related papers: The Falling Time of an Inverted Plane Pendulum
The paper presents a discussion on the asymptotic formula for the number of plane partitions of a large positive integer.
We give a formula for the inverse matrix to an infinite matrix with possibly noncommutative entries, generalizing the Newton interpolation formula and the Taylor formula.
We derive new upper limits on the ellipticity of pulsars whose braking index has been measured, more tightening than those usually given, assuming that both a gravitational torque and an electromagnetic one act on them. We show that the…
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.
The classic simple pendulum is a device which works as a simple harmonic oscillator (S.H.M.) only approximately. The time period remains fixed as long as the amplitude is kept sufficiently small. This limitation makes it unsatisfactory…
We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
We describe the correct cubic relation between the mass configuration of a Kater reversible pendulum and its period of oscillation. From an analysis of its solutions we conclude that there could be as many as three distinct mass…
We obtain a novel connection between the exact solutions of the plane pendulum, hyperbolic plane pendulum and inverted plane pendulum equations as well as the static solutions of the sine-Gordon and the sine hyperbolic-Gordon equations and…
The model of weak measurements is applied to various problems, related to the time problem in quantum mechanics. The review and generalization of the theoretical analysis of the time problem in quantum mechanics based on the concept of weak…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
We find an upper estimate for a splitting time of a thin parallel beam for irrational triangle billiards in terms of some number-theoretic function of angles. We provide an upper estimate on this function for some class of angles.
In this work we solve the nonlinear second order differential equation of the simple pendulum with a general initial angular displacement ($\theta(0)=\theta_0$) and velocity ($\dot{\theta}(0)=\phi_0$), obtaining a closed-form solution in…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of $N$ sines with different frequencies and phases. We show that when the amplitude is scaled with the…
Revisiting canonical integration of the classical pendulum around its unstable equilibrium, normal hyperbolic canonical coordinates are constructed
This paper proves a reciprocity formula for modular inverses for non-zero integers and demonstrates some applications of the reciprocity formula in calculating or verifying some modular inverses of specific forms, including the modular…
In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove…
The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and…