Routh reduction presents the minimum number of differential equations that uniquely describe the state of nonlinear mechanical systems where the state variables can be separated into essential ones and cyclic ones. This work extends Routh reducibility for a relevant set of controlled mechanical systems. A chain of theorems is presented for identifying the conditions when reduced order rank conditions can be applied for determining the Kalman controllability of Routh reducible mechanical systems where actuation takes place along the cyclic coordinates only, while some of the essential coordinates and their derivatives are observed. Four mechanical examples represent the advantages of using reduced rank conditions to check and/or to exclude linear controllability in such systems.
The mixing of granular materials in an agitated drum can be characterized by the dimensionless power equation. The equation was created by dimensional analysis, for which the parameters affecting the mixing power requirement were collected based on the literature. The most important of these are the rotational speed, the drum loading factor, the geometric and physical properties of the mixing drum and the granular materials. The dimensionless power equation is used to estimate with reasonable accuracy the Power number within the given range of applicability , which has been validated by measurements. From the Power number, the mixing power requirement of the mixed granular material can be calculated, which can be used as operational data for selecting the mixing motor.
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