In 1890 German mathematician and physicist W. Hess found new special case of integrability Euler - Poisson equations motion a heavy rigid body with fixed point. 1892 P. A. Nekrasov proved that the solution problem point under conditions reduces to integrating second order linear differential equation. this paper corresponding equation is derived its coefficients are presented in rational form. ...

1 Problem It is generally considered that systems with friction are not part of Hamiltonian dynamics, but this is not always the case. Show that a (nonrelativistic) damped harmonic oscillator can be described by a Hamiltonian (and by a Lagrangian), with the implication that Liouville's theorem applies here. Consider motion in coordinate x of a particle of mass m with equation of motion, m¨x + β...

It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficult...

A direct method called fixation is introduced for solving the general motion vision problem, arbitrary motion relative to an arbitrary environment. This method results in a linear constraint equation which explicitly expresses the rotational velocity in terms of the translational velocity. The combination of this constraint equation with the Brightness-Change Constraint Equation solves the gene...

piezoelectric microcantilevers (mcs) are a new generation of microbeams used in atomic force microscopes (afms). due to their miniaturization of afms as well as their increased imaging precision and speed, these mcs are more popular than their classical counterparts. given the widespread application of these beams in nanoparticle topography, analysis of their vibrating motion has attracted much...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

This paper is intended to reveal some new aspects of the principle of work and energy in its differential form. A theorem is given to state the principle of work and energy in differential form that can be applied alone to build up all the dynamical equations of a special class of MDOF mechanical systems. Some illustrations and discussions are presented to demonstrate the refined applicability ...