Finding the relative trajectory of the cargo in the body of a vehicle which is going down or up on a curved section of the road

Abstract

With a certain assumption, the load, which during relative movement along the bottom of the body makes translational movement, can be taken as a material point. In this case, finding the relative movement of the load in the body when the car moves along the road with a spatial axis is reduced to finding the relative trajectory of the material point.

In known works, it is proposed to use the accompanying trihedron of the trajectory of the transfer motion and Frenet's formula to find the absolute acceleration vector of a point. The independent variable is not time, as in traditional problems, but the arc coordinate of the transfer trajectory, since only under this condition can Frenet's formulas be applied. The vector of absolute acceleration is obtained in projections onto the vertices of the moving accompanying trihedron, without looking for individual components (transfer, relative, and Coriolis acceleration), as is done in traditional approaches.

The purpose of the study is to investigate the relative movement of the load, taken as a material point, along the bottom of the body of a truck moving along a curvilinear section of the road with a spatial axis during its ascent or descent.

The spatial curve is characterized by two parameters that depend on the kinematics of the accompanying Frenet trihedron. These parameters are the curvature k and the twist σ of the curve. Their values at any point of the curve will be determined if the dependencies k=k(s) and σ=σ(s) are known, where s is the arc coordinate (the arc length of the curve). It is assumed that such a spatial curve is the axis of a curved section of the road that goes uphill or downhill.

The application of the accompanying trihedron of the curve and Frenet's formulas made it possible to describe the relative motion of the cargo in the body of a car moving along a road having a spatial axis with constant and variable speeds. The regularities of the relative movement of the cargo when the car is moving on the road, the axis of which is a helical line with constant curvature and twist, have been found. It was found that there is no significant difference between the value of the relative speed of the cargo when the car moves at a constant speed down or uphill at the initial stage. When braking on a descent, a significant relative movement of the cargo is observed, which increases with an increase in the braking acceleration, and when climbing, on the contrary, the relative movement decreases with an increase in the braking acceleration. The regularity of the relative movement of the cargo when the car moves along the road with variable curvature and torsion of the axis line depends on the type of these dependencies as a function of the length of the arc of the axis line.

Key words: accompanying Frenet trihedron, the bottom of the car body, the trajectory of the load, the speed of the load, the length of the arc of the axis line