VIEWPOINTS ON SOME VIBRATION FEATURES OF THE RAILWAY TRACTION UNITS THE BRACHISTOCRONA PROBLEM

Abstract

A Brachistochrone curve (Gr. βραχίστος, brachistos - the shortest, χρόνος, chronos - time), or curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and is constrained to move along the curve to the second point, under the action of constant gravity and assuming no friction. For less dynamic oscillations of a locomotive in case of jump and galop at high speeds and for limiting damper amplitudes it is a must that for any point on the suspension, the trajectory described during a half oscillation should be as short as possible. The virtual distance covered by a certain point on the suspension is a curve. The point trajectory may be comparative to a epicicloide equation. It is identified the plane curve of the point considered in the suspension plan - the brachistocrona problem, finding that curve in the family of plane curves conecting the two points A and B (the trajectory oscilation extremities). A material point leaving origin A with null initial speed, is subject to a force and reaches point B in the shortest time.