Related papers: Analytical solution of the Euler-Poinsot problem
The continuous point symmetry algebra of the hyperbolic Ernst equation is presented. In a second step the corresponding group transformations are considered. Accordingly, the solutions of the hyperbolic Ernst equation that are invariant…
We consider stochastic versions of Euler--Arnold equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden. For the Euler equation on a compact manifold (possibly with smooth boundary) we establish local…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
A continuous solution is proposed to the problem of uniform global exponential estimation of the angular velocity for rigid bodies by means of direct attitude measurements. The proposed observer is designed on…
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…
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are…
We investigate a singularly perturbed, non-convex variational problem arising in materials science with a combination of geometrical and numerical methods. Our starting point is a work by Stefan M\"uller, where it is proven that the…
One of the main objectives of science is the recognition of a general pattern in a particular phenomenon in some particular regime. In this work, this is achieved with the analytical expression for the optimal protocol that minimizes the…
This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical…
We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogo- nal functions defined on…
The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical…
In this manuscript, we present analytical external spherical solutions of entangled relativity, which we compare to numerical solutions obtained in a Tolman-Oppenheimer-Volkoff framework. Analytical and numerical solutions match perfectly…
The paper proposes a technique to estimate the angular velocity of a rigid body from single vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead,…
This paper presents an alternative way to the dynamic modeling of a rotational inverted pendulum using the classic mechanics known as Euler-Lagrange allows to find motion equations that describe our model. It also has a design of the basic…
The paper proposes a technique to estimate the angular velocity of a rigid body from vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler-Lagrange equations. Hamel's equations, on the…
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic…