## 2 Materials and Methods
Point \(O\) denotes the rotation center of the considered thrower, and we will limit blade length to segment \(AB\). The thrower's rotation direction in the equivalent scheme is shown by an arrow. Figure 1: Structural and technological scheme of the haulm harvester, with an improved loading mechanism: 1—frame; 2—copying wheel; 3—rotary haulm removing unit; 4—blade thrower; 5—unloading pipe; 6—preliminary root head cutter; 7—drive of the working bodies. First, consider the movement of haulm particle \(M\) along the thrower blade. We choose as the blade's initial position the time moment when its outer end is located at the lowest point of the possible motion trajectory (point \(B\)). For a certain period of time \(t\) the blade, together with the haulm, moving along it, turn by a certain angle \(\varphi\), where \(\varphi=\omega\cdot t\) and \(\omega\) is the angular velocity of rotation of the thrower. In this case point \(B\) will move into point \(B^{\prime}\). We will show, on an equivalent scheme, the necessary angular parameters of the considered mechanical system. Let \(\psi\) be the angle between the throwing blade and radius, which is drawn through the rotation axis (point \(O\)) and haulm particle (point \(M\)), moving along the blade surface at an arbitrary time moment \(t\). We will regard two extreme values of angle \(\psi\). Staring position \(\psi_{0}\) corresponds to the value of angle \(\psi\) when point \(M\) coincides with point \(A\) (or point \(A^{\prime}\)). The final position \(\psi_{1}\) is the value of angle \(\psi\) in a position when point \(M\) coincides with point \(B\) (or point \(B^{\prime}\) in an arbitrary position of the blade). Obviously, during the rotation, the blade angles \(\psi_{0}\) and \(\psi_{1}\) remain constant. They depend only on the location of the blade relative to the radial direction in the plane of the thrower. Thus, the following inequality \(\psi_{1}\leq\psi\leq\psi_{0}\) holds for angle \(\psi\). We will denote \(\beta\)--the angle between the blade surface and some vertical line at arbitrary time \(t\). All the angles \(\psi_{0}\), \(\psi\), \(\psi_{1}\) and \(\beta\) are shown in the equivalent scheme (Figure 2). As evident from the equivalent scheme, a relationship takes place: \(\psi_{0}\), \(\psi\), \(\psi_{1}\) and \(\beta\). To describe the relative motion of a haulm particle along throwing blade \(AB\), we introduce a flat Cartesian coordinate system \(xAy\). The axis \(Ax\) is directed along the blade, and the axis \(Ay\) is perpendicular to the plane of this blade, and the axis \(Ay\) passes through the rotation center of thrower (point \(O\)). The origin of the coordinate system \(xAy\) is located at the place where the blade is attached to the drive shaft (point \(A\)). Let us define the necessary geometric relationships between the parameters of the thrower. As can be seen from the equivalent scheme (Figure 2), we have the following relationships:  
\[x=r\cdot\cos\psi-r_{0}\cdot\cos\psi_{0} \tag{1}\]  
and  
\[r\cdot\sin\psi=r_{0}\cdot\sin\psi_{0}=\text{const} \tag{2}\]  
where \(r\) is the current radius of the position of point \(M\) relative to the disk center (point \(O\)) at an arbitrary moment in time \(t\). Figure 2: Equivalent scheme of haulm particle movement process along the throwing blade surface. In order to draw up a differential equation for the movement of the considered beet tops particle \(M\) along the blade surface, it is necessary to indicate in an equivalent scheme all forces acting on the beet tops particle during its translational movement and to determine their values. First of all, we distinguish the force of weight of haulm particle \(M\), which is equal to:  
\[G=m\cdot g \tag{3}\]  
where \(m\) is the mass (weight) of haulm particle; \(g\) is the gravity acceleration.