In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a space station (www.youtube.com/watch?v=L2o9eBl_Gzw) and the tennis racket phenomenon (www.youtube.com/watch?v=4dqCQqI-Gis). These phenomena are described by Euler’s equation of an unconstrained rigid body that has three distinct values of moments of inertia. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, especially for students, we investigate the phenomena using more precise mathematical and graphical tools than those employed previously. Following Élie Cartan [1], we explicitly write the vector basis of a body-attached, moving coordinate system. Using this moving frame method, we describe the Newton and Euler equations. The adoption of the moving coordinate frame expresses the rotation of the body more clearly and allows us to use the Lie group theory of special orthogonal group SO(3). We integrate the torque-free Euler equation using the fourth-order Runge-Kutta method. Then we apply a recovery equation to obtain the rotation matrix for the body. By combining the geometrical solutions with numerical simulations, we demonstrate that the unexpected rotations observed in the Dzhanibekov and the tennis racket experiments preserve the conservation of angular momentum.
In search of guaranteeing global energy requirements, waste from different agricultural, forestry and industrial sources is presented as a renewable and sustainable energy source. The manufacture of solid fuels from biomass based on the densification of this to improve its mechanical and energy properties is one of the mechanisms of viable energy production from the technical-economic point of view. The biomass mixture is one of the topics currently researched, in which various factors can affect the final behavior of the briquettes. In this research the influence on the mechanical properties of briquettes obtained from the mixture between two biomasses is studied: rice husk and pine sawdust. A mixed factorial experimental factorial design is used, in which the process temperature, the proportion of the rice husk biomass over the total mass, and the compaction time are defined as experimental factors. Experimental statistical models are obtained that partially explain the behavior of several responses that characterize the mechanical properties of the briquettes based on the selected independent parameters. It was found that the mechanical durability of the briquettes is higher than 97.5%, meets the existing standards, like German Institute for Standardization (DIN) 51731, Theological Institute Batista Ebenézer (ITEBE) SS187120 or International Organization for Standardization (ISO) 17225-2, for a compaction temperature of 110 °C and a proportion of rice husk that does not exceed 60% of the total biomass mixture in the briquette. The compaction time was also statistically significant to achieve a briquettes density and an appropriate elasticity modulus in the briquettes. The results of this research are of interest and can serve as a starting point for the design of the industrial process of densification of these two mixed biomasses.
This paper presents a complete explanation of the Dzhanibekov and the tennis racket phenomena. These phenomena are described by Euler's equation for an unconstrained rigid body that has three distinct moment of inertia values. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, the phenomenon is investigated using more precise mathematical and graphical tools than those employed previously. The torque-free Euler equations are integrated using the fourth-order Runge–Kutta method. Then, a recovery equation is applied to obtain the rotation matrix for the body. By combining the geometrical solutions with numerical simulations, the unexpected rotations observed in the Dzhanibekov and the tennis racket experiments are shown to preserve the conservation of angular momentum.
In this paper a study on the process of densification of oil palm empty fruit bunches (OPEFB) is presented. An empirical-statistical model that allows the evaluation of densification process is obtained through an experimental factorial design. The main purpose of the experimental arrangement is to find the appropriate reference values for the experimental factors - moisture content, fiber length and compaction time-with which optimal performance responses of briquettes are achieved. Statistical models are obtained that explain in an acceptable way the influence of independent experimental factors on the mechanical properties of briquettes, such as briquettes density, durability index and compressive strength. It is possible to conclude that briquettes manufactured with the appropriate reference values, moisture content of 8% w.b., fiber length of 73.6 mm and a compaction time of 26.6 s respectively, meet mechanical and thermal requirements that are required in the most representative standards for biomass briquettes for energy purposes. Results obtained in the current investigation can be used as reference for the design of an industrial pilot plant destined to the densification of EFB of African oil palm.
The objective of this research is to develop an experimental-theoretical analysis about the influence of the cooling medium and the geometry of the welding bead profile in fatigue life and the associated parameters with structural integrity of welded joints. A welded joint with cruciform geometry is considered using SMAW (Shielded Metal ArcWelding), plates in structural steel ASTM A36 HR of 8 mm of thickness, and E6013 electrode input. A three-dimensional computational model of the cruciform joint was created using the finite element method. For this model, the surface undulation of the cord and differentiation in the mechanical properties of the fusion zone were considered, the heat-affected zone (HAZ) and base material, respectively. In addition, an initial residual stress field, which was established experimentally, was considered. The results were a set of analytical expressions for the weld magnification factor Mk. It was found that values for the latter decrease markedly in function of the intensity of the cooling medium used in the post welding cooling phase, mainly due to the effect of the residual compressive stresses. The obtained models of behavior of the weld magnification factor are compared with the results from other researchers with some small differences, mainly due to the inclusion of the cooling effect of the post weld and the variation of the leg of the weld bead. The obtained analytical equations in the present research for Mk can be used in management models of life and structural integrity for this type of welded joint.
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