08. Creation of equations of movement of material particle on a plane inclined to vertical spinning axis

Smaglij V. I.
Pages: 40-44.

Full article: 
Abstract
Goal. Output the equation of motion of a material particle on a rough plane, set at an angle to the vertical axis of its rotation. Methods. A general equation of motion of a particle in a plane inclined to the vertical axis of rotation is obtained, using the equation of the second kind of Lagrange, and the equation of transition to a moving coordinate system, which rotates along with the plane, is used. Results The physical model of motion of a particle is developed and the equation of motion of a material particle on a rough plane, set at an angle to the vertical axis of its rotation, is derived. Conclusions The obtained equations are transformed into known equations of motion of a particle along a rough horizontal plane, as well as on a rough vertical plane at vertical axes of their rotation, which confirms the correctness of the equations obtained for describing the movement of fertilizer particles along the lower shelf of the vanes of the centrifugal spreading of the tufts.

Key words: Lagrange equation of the second kind, moving coordinate system, rotation, reaction forces, friction, mass, acceleration, derivative, substitution, transformation, analysis.

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