Related papers: The Exact Solution of Lagrange's Gyroscope
Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse $N$ and the Riemann tensor takes the form $R^{t}_{.itj}=-k_{i}k_{j}, i,j=1,2,3$; thus these solutions…
Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field,…
The Dirac equation is solved in the rotating Bertotti-Robinson spacetime. The set of equations representing the Dirac equation in the Newman-Penrose formalism is decoupled into an axial and angular part. The axial equation, which is…
In an attempt to look for the root of nonstandard Lagrangians in the theories of the inverse variational problem we introduce a logarithmic Lagrangian (LL) in addition to the so-called reciprocal Lagrangian (RL) that exists in the…
We use a fractional transformation to connect the traveling wave solutions of the nonlinear Schr\"odinger equation (NLSE), phase-locked with a source, to the elliptic functions satisfying, $f^{\prime\prime}\pm af\pm \lambda f^{3}=0$. The…
We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions…
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\chi_2$ type nonlinearity as well as two mode…
Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D {\bf 80}, 064021 (2009)], the gravitational radiation reaction to Lagrange's equilateral triangular solution of the three-body problem is investigated in an…
Exact solutions are found for Euler's equations of rigid body motion for general asymmetrical bodies under the influence of torque by using Jacobi elliptic functions. Differential equations are determined for the amplitudes and the…
The Colombo top is a basic model in the rotation dynamics of a celestial body moving on a precessing orbit and perturbed by a gravitational torque. The paper presents a detailed study of analytical solution to this problem. By solving…
It is known that difference equations generated as the Newton-Raphson iteration for quadratic equations are solvable in closed form, and the solution can be constructed from linear three-term recurrence relations with constant coefficients.…
In this paper, a fully implicit Crank-Nicolson discontinuous Galerkin method is proposed for solving the Ginzburg-Landau equation. By leveraging a novel analytical technique, we rigorously establish the unique solvability of the constructed…
In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the…
In this article, we derive the exact closed-form solution for the displacement in the interior of an elastic half-space due to a buried point force with Heaviside step function time history. It is referred to as the tensor Green's function…
The family of exactly solvable potentials for Newton's equation of motion in the one-dimensional system with quadratic drag force has been determined completely. The determination is based on the implicit inverse-function solution valid for…
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to…
We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into…
The Landau-Lifshitz form of the Lorentz-Abraham-Dirac equation in the presence of a plane wave of arbitrary shape and polarization is solved exactly and in closed form. The explicit solution is presented in the particular, paradigmatic…
The null geodesics that describe photon orbits in the spacetime of a rotating electrically charged black hole (Kerr-Newman) are solved exactly including the contribution from the cosmological constant. We derive elegant closed form…