Equations of motion of masses of the Chelomey pendulum model

To verify the provisions stated by V.I. Bogomolov, B.I. Puzanov. and Linevich E.I. about the possibility of performing over-unit work by inertial forces, a closed mechanical system in the form of kinematically connected rotating masses is proposed for consideration. The research aimed, within the framework of Newtonian mechanics, to study the fulfillment of the laws of conservation of momentum, angular momentum and energy, to establish the possibility of performing work by inertial forces (centrifugal and Coriolis), to assess the change in kinetic parameters using the example of the Chelomey pendulum model. For the complex radial-circular motion of the masses of the Chelomey pendulum model, resolving equations are obtained. To verify the analytical calculations, algorithms for numerical solutions of the above problems have been developed and implemented in the MathCAD software package

An Assessment of the Application of Bernoulli’s Theorem in the Generation of Lift Force

In this paper, we will be performing a detailed analysis of the application of Bernoulli’s Theorem in aviation and aerodynamics. The aim of our experiment and consequently this paper is to verify the application of Bernoulli’s Theorem in the aviation industry. In the field of aerodynamics, Bernoulli’s Theorem has been specifically used in shaping the wings of an aircraft. Over the years, however there has been a significant controversy in the aviation industry regarding the generation of lift force, especially the applicability of Newton’s Third Law of Motion along with Bernoulli’s Theorem. The controversy seems to be due to a combined effect of Newton’s and Bernoulli’s theorems’ (e.g. ‘Equal Transit Time Theory’), which may be incorrectly applied in the real world. Further, it seems that people are over-simplifying the problem of aerodynamic lift leading to the dismissal of either one of the theorems, when in reality both the theorems seem to be at play, as explained in this paper. For the generation of lift in air, momentum, mass and energy need to be conserved. Newton’s laws take into account the conservation of momentum, whereas Bernoulli’s Theorem considers the conservation of energy. Hence, they are both relevant for the generation of lift in air. However, no one has been able to determine accurately the working of both these theorems in the process of providing lift to an aircraft. Through this research paper, we have been able to prove the effect of Bernoulli’s Theorem in generating lift in air.

Numerical study of mixing index in offset inlets 3-D T mixer with bend shape mixing channel

The objective of this paper is the computational analysis on the mixing index of simple T shape mixer, offset inlets T shape mixer, and offset inlets T mixer with bend shape mixing channel by CFD simulation. Computational fluid dynamics software package solves conservation of mass equation, conservation of momentum equation, and conservation of energy equation. In the case of offset inlets T shape mixer, as the aspect ratio (height to width ratio) of mixing channel increased so mixing quality also increased and offset inlets T mixer with bend shape is a combination of increased aspect ratio as well as chaotic advection mechanisms, so it provides advanced mixing index than offset inlets T shape mixer and simple T shape mixer. Pressure fall in offset inlets T shape mixer is excess than simple T shape mixer but narrowly degraded than offset inlets T mixer with bend shape. Chaotic advection rooted microchannel generates secondary flow because of which motives a high-pressure drop in the microchannel.

Equations of motion of masses of the Chelomey pendulum model

To verify the provisions stated by V.I. Bogomolov, B.I. Puzanov. and Linevich E.I. about the possibility of performing over-unit work by inertial forces, a closed mechanical system in the form of kinematically connected rotating masses is proposed for consideration. The research aimed, within the framework of Newtonian mechanics, to study the fulfillment of the laws of conservation of momentum, angular momentum and energy, to establish the possibility of performing work by inertial forces (centrifugal and Coriolis), to assess the change in kinetic parameters using the example of the Chelomey pendulum model. For the complex radial-circular motion of the masses of the Chelomey pendulum model, resolving equations are obtained. To verify the analytical calculations, algorithms for numerical solutions of the above problems have been developed and implemented in the MathCAD software package.

A Refined Well-Posedness Result for the Modified KdV Equation in the Fourier–Lebesgue Spaces

We study the well-posedness of the complex-valued modified Korteweg-de Vries equation (mKdV) on the circle at low regularity. In our previous work (2021), we introduced the second renormalized mKdV equation, based on the conservation of momentum, which we proposed as the correct model to study the complex-valued mKdV outside $$H^\frac{1}{2}({\mathbb {T}})$$ H 1 2 ( T ) . Here, we employ the method introduced by Deng et al. (Commun Math Phys 384(1):1061–1107, 2021) to prove local well-posedness of the second renormalized mKdV equation in the Fourier–Lebesgue spaces $${\mathcal {F}}L^{s,p}({\mathbb {T}})$$ F L s , p ( T ) for $$s\ge \frac{1}{2}$$ s ≥ 1 2 and $$1\le p <\infty $$ 1 ≤ p < ∞ . As a byproduct of this well-posedness result, we show ill-posedness of the complex-valued mKdV without the second renormalization for initial data in these Fourier–Lebesgue spaces with infinite momentum.

Experiments on rebounding slow impacts under asteroid conditions

&lt;p class=&quot;p1&quot;&gt;&lt;span class=&quot;s1&quot;&gt;The&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;surfaces&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;of&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;rubble-pile&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;asteroids&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;are&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;covered&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;in&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;regolith of a variety of sizes.&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;In some cases like for the asteroid Itokawa, the size distribution of regolith is not uniform across the surface [1]. Some areas are dominated by finer grains, while other areas are covered by larger rocks.&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;There are a number of competing explanations for this observed size segregation [2&amp;#8211;4]. One approach is the so called ballistic-sorting-effect [2], where impacting particles sort themselves through different rebound behavior.&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;p1&quot;&gt;&lt;span class=&quot;s1&quot;&gt;In our work we want to set practical limits on the role ballistic sorting can play in shaping an asteroids surface. To this end we conduct a series of drop tower experiments examining the impact kinetics of slow (cm/s)&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;3 mm sized projectiles into a regolith surface under conditions realistic for asteroid surfaces, i.e. vacuum and low gravity. We track the impactor with high-speed cameras and determine its velocity in 3 dimensions before and after the impact. From these velocities, we can then compute a coefficient of restitution (COR).&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;We then repeat the experiment for surfaces composed of differently sized material.&lt;span class=&quot;Apple-converted-space&quot;&gt;&amp;#160; &lt;/span&gt;We find that for a regolith bed made from particles of similar size as the impactor we get a lower COR (0,1) than for beds made up of significantly larger (0,5) or smaller particles (0,8). The more elastic collisions for larger sized targets follows from conservation of momentum. For the finer material we suggest that the higher COR is a function of interparticle adhesion.&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;p1&quot;&gt;&lt;span class=&quot;s1&quot;&gt;[1] A. Fujiwara, J. Kawaguchi, D.K. Yeomans, M. Abe, T. Mukai, T. Okada, J. Saito, H. Yano, M. Yoshikawa, D.J. Scheeres et al., Science 312, 1330 (2006)&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;p1&quot;&gt;&lt;span class=&quot;s1&quot;&gt;[2] T. Shinbrot, T. Sabuwala, T. Siu, M.V. Lazo, P. Chakraborty, Phys. Rev. Lett. 118, 111101 (2017)&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;p1&quot;&gt;&lt;span class=&quot;s1&quot;&gt;[3] S. Matsumura, D.C. Richardson, P. Michel, S.R. Schwartz, R.L. Ballouz, Mon. Not. the R. Astron. Soc. 443, 3368 (2014)&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;p1&quot;&gt;&lt;span class=&quot;s1&quot;&gt;[4] A.J. Dombard, O.S. Barnouin, L.M. Prockter, P.C. Thomas, Icarus 210, 713 (2010)&lt;/span&gt;&lt;/p&gt;