The brachistochronic motion of a wheeled vehicle

Abstract

The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin's maximum principle and singular optimal control theory.

Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field

“…The sign that tells which system of equations to use at the initial moment.The motion of the slider M 2 will stop in the case when the absolute value of the resultant of the active forces acting on the slider M 2 is less than the force of the Coulomb friction force of the slider and also at rest.Using an example of a simple system models, papers [13] and [14] provide calculation of the minimum value of the coefficient of friction using the Coulomb laws of friction sliding. In [15] and [16] a deeper look into the necessary dynamic conditions, for the realization of motion in accordance with the system constraints, can be found. In case when 2 0…”