The paper deals with a suitable transformation related to the metric scalar of hyper-surface so that Raychaudhuri Equation (RE) can be written as second order nonlinear differential equation. A first integral this equation gives possible analytic solution RE. Also, it is shown construction Lagrangian (and hence Hamiltonian) possible, from which RE derived. Wheeler-Dewitt has been formulated in ...

Abstract We show a connection between global unconstrained optimization of continuous function f and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution v the critical Hamilton–Jacobi is built by small discount approximation as well long time limit associated evolutive equation. Then represented value control problem with target, whose optimal trajectories a...

The random intensity of noise approach to the one-dimensional Laval-Dubrulle-Nazarenko-type model having deductive support from the three-dimensional Navier-Stokes equation is used to describe Lagrangian acceleration statistics of a fluid particle in developed turbulent flows. Intensity of additive noise and cross correlation between multiplicative and additive noises entering a nonlinear Lange...

Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the equivalent Lagrangians play an important role because they admit the same Euler-Lagrange equations. By adding a total time derivative of a suitable function to a g...

We describe a class of mechanical systems for which the “method of controlled Lagrangians” provides a family of control laws that stabilize an unstable (relative) equilibrium. The controlled Lagrangian approach involves making modifications to the Lagrangian for the uncontrolled system such that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the close...